Sc.B. Brown 1977, Ph.D. Harvard 1982, Moore Instructor M.I.T. 1982-85, NSF Postdoc 1983-86, Assoc. Prof. Boston University 1986-88, Assoc. Prof. Brown University, 1988-1991, Professor of Mathematics Brown University 1991-present, Math Dept Chair 2001-04, 2008, Royce Family Professor of Teaching Excellence 2014-2017. Primary interests are number theory, elliptic curves, arithmetic geometry, arithmetic dynamics, and cryptography. Author of 8 textbooks and research monographs and more than 100 research articles.
Doyle, John R., Silverman, Joseph H. "A uniform field-of-definition/field-of-moduli bound for dynamical systems on PN." Journal of Number Theory, vol. 195, 2019, pp. 1-22. |
Silverman, Joseph H., Call, Gregory S. "Degeneration of dynamical degrees in families of maps." Acta Arithmetica, vol. 184, no. 2, 2018, pp. 101-116. |
Silverman, Joseph. "Good reduction and Shafarevich-type theorems for dynamical systems with portrait level structures." Pacific Journal of Mathematics, vol. 295, no. 1, 2018, pp. 145-190. |
Silverman, Joseph H. "Divisor divisibility sequences on tori." Acta Arithmetica, vol. 177, no. 4, 2017, pp. 315-345. |
Bridy, Andrew, Ingram, Patrick, Jones, Rafe, Juul, Jamie, Levy, Alon, Manes, Michelle, Rubinstein-Salzedo, Simon, Silverman, Joseph H. "Finite ramification for preimage fields of post-critically finite morphisms." Mathematical Research Letters, vol. 24, no. 6, 2017, pp. 1633-1647. |
Silverman, Joseph H. "Rational points on, and the arithmetic of, elliptic curves: A tale of two books (and an article)." Bulletin of the American Mathematical Society, vol. 54, no. 4, 2017, pp. 591-594. |
Kawaguchi, Shu, Silverman, Joseph H. "On the dynamical and arithmetic degrees of rational self-maps of algebraic varieties." Journal für die reine und angewandte Mathematik (Crelles Journal), vol. 2016, no. 713, 2016. |
Kawaguchi, Shu, Silverman, Joseph H. "Dynamical canonical heights for Jordan blocks, arithmetic degrees of orbits, and nef canonical heights on abelian varieties." Trans. Amer. Math. Soc., vol. 368, no. 7, 2015, pp. 5009-5035. |
Kawaguchi, Shu, Silverman, Joseph H. "Examples of dynamical degree equals arithmetic degree." Michigan Math. J., vol. 63, no. 1, 2014, pp. 41-63. |
Hoffstein, Jeff, Pipher, Jill, Schanck, John M., Silverman, Joseph H., Whyte, William. "Transcript Secure Signatures Based on Modular Lattices." Post-Quantum Cryptography, 2014, pp. 142-159. |
Silverman, Joseph H., Viray, Bianca. "On a uniform bound for the number of exceptional linear subvarieties in the dynamical Mordell-Lang conjecture." Mathematical Research Letters, vol. 20, no. 3, 2013, pp. 547-566. |
Silverman, Joseph H. "Primitive divisors, dynamical Zsigmondy sets, and Vojtaʼs conjecture." Journal of Number Theory, vol. 133, no. 9, 2013, pp. 2948-2963. |
Silverman, Joseph H. "WHAT IS...the p-adic Mandelbrot Set?." Notices Amer. Math. Soc., vol. 60, no. 08, 2013, pp. 1. |
INGRAM, PATRICK, MAHÉ, VALÉRY, SILVERMAN, JOSEPH H., STANGE, KATHERINE E., STRENG, MARCO. "ALGEBRAIC DIVISIBILITY SEQUENCES OVER FUNCTION FIELDS." J. Aust. Math. Soc., vol. 92, no. 01, 2012, pp. 99-126. |
Silverman, Joseph H. "An algebraic approach to certain cases of Thurston rigidity." Proceedings of the American Mathematical Society, vol. 140, no. 10, 2012, pp. 3421-3434. |
Silverman, Joseph H. "Book Review: Some problems of unlikely intersections in arithmetic and geometry." Bulletin of the American Mathematical Society, vol. 50, no. 2, 2012, pp. 353-358. |
SILVERMAN, JOSEPH H. "Dynamical degree, arithmetic entropy, and canonical heights for dominant rational self-maps of projective space." Ergod. Th. Dynam. Sys., vol. 34, no. 02, 2012, pp. 633-664. |
Silverman, Joseph H. "Elliptic Carmichael numbers and elliptic Korselt criteria." Acta Arithmetica, vol. 155, no. 3, 2012, pp. 233-246. |
Silverman, Joseph H. "Lehmer’s conjecture for polynomials satisfying a congruence divisibility condition and an analogue for elliptic curves." J. Théor. Nombres Bordeaux, vol. 24, no. 3, 2012, pp. 751-772. |
Hsia, Liang-Chung, Silverman, Joseph. "A quantitative estimate for quasiintegral points in orbits." Pacific Journal of Mathematics, vol. 249, no. 2, 2011, pp. 321-342. |
Silverman, Joseph H., Stange, Katherine E. "Amicable Pairs and Aliquot Cycles for Elliptic Curves." Experimental Mathematics, vol. 20, no. 3, 2011, pp. 329-357. |
Silverman, Joseph H., Stange, Katherine E. "Terms in elliptic divisibility sequences divisible by their indices." Acta Arithmetica, vol. 146, no. 4, 2011, pp. 355-378. |
Silverman, Joseph H. "A Survey of Local and Global Pairings on Elliptic Curves and Abelian Varieties." Automata, Languages and Programming, 2010, pp. 377-396. |
Silverman, Joseph. "Local-global aspects of (hyper)elliptic curves over (in)finite fields." Advances in Mathematics of Communications, vol. 4, no. 2, 2010, pp. 101-114. |
Silverman, Joseph H., Voloch, José Felipe. "A local-global criterion for dynamics on P 1." Acta Arithmetica, vol. 137, no. 3, 2009, pp. 285-294. |
Kawaguchi, Shu, Silverman, Joseph H. "Canonical Heights and the Arithmetic Complexity of Morphisms on Projective Space." Pure and Applied Mathematics Quarterly, vol. 5, no. 4, 2009, pp. 1201-1217. |
Silverman, Joseph H. "Lifting and Elliptic Curve Discrete Logarithms." Automata, Languages and Programming, 2009, pp. 82-102. |
Hsia, Liang-Chung, Silverman, Joseph. "On a dynamical Brauer–Manin obstruction." J. Théor. Nombres Bordeaux, vol. 21, no. 1, 2009, pp. 235-250. |
Kawaguchi, Shu, Silverman, Joseph H. "Nonarchimedean Green functions and dynamics on projective space." Mathematische Zeitschrift, vol. 262, no. 1, 2008, pp. 173-197. |
INGRAM, PATRICK, SILVERMAN, JOSEPH H. "Primitive divisors in arithmetic dynamics." Mathematical Proceedings of the Cambridge Philosophical Society, vol. 146, no. 02, 2008, pp. 289. |
Kawaguchi, S., Silverman, J. H. "Dynamics of projective morphisms having identical canonical heights." Proceedings of the London Mathematical Society, vol. 95, no. 2, 2007, pp. 519-544. |
Rosen, Michael, Silverman, Joseph H. "On the independence of Heegner points associated to distinct quadratic imaginary fields." Journal of Number Theory, vol. 127, no. 1, 2007, pp. 10-36. |
Silverman, Joseph H. "Height Bounds and Preperiodic Points for Families of Jointly Regular Affine Maps." Pure and Applied Mathematics Quarterly, vol. 2, no. 1, 2006, pp. 135-145. |
Silverman, Joseph H., Whyte, William. "Timing Attacks on NTRUEncrypt Via Variation in the Number of Hash Calls." Automata, Languages and Programming, 2006, pp. 208-224. |
Silverman, Joseph H. "Addendum to “p-adic properties of division polynomials and elliptic divisibility sequences”." Mathematische Annalen, vol. 332, no. 2, 2005, pp. 473-474. |
Silverman, J. H., Smart, N. P., Vercauteren, F. "An Algebraic Approach to NTRU (q = 2 n ) via Witt Vectors and Overdetermined Systems of Nonlinear Equations." Automata, Languages and Programming, 2005, pp. 278-293. |
Howgrave-Graham, Nick, Silverman, Joseph H., Whyte, William. "Choosing Parameter Sets for NTRUEncrypt with NAEP and SVES-3." Automata, Languages and Programming, 2005, pp. 118-135. |
Silverman, Joseph H. "Generalized Greatest Common Divisors, Divisibility Sequences, and Vojta’s Conjecture for Blowups." Mh Math, vol. 145, no. 4, 2005, pp. 333-350. |
Baker, Matthew H., Silverman, Joseph H. "A lower bound for the canonical height on abelian varieties over abelian extensions." Mathematical Research Letters, vol. 11, no. 3, 2004, pp. 377-396. |
Silverman, Joseph H. "A lower bound for the canonical height on elliptic curves over abelian extensions." Journal of Number Theory, vol. 104, no. 2, 2004, pp. 353-372. |
Silverman, Joseph H. "Common divisors of elliptic divisibility sequences over function fields." manuscripta mathematica, vol. 114, no. 4, 2004. |
Silverman, Joseph H. "p-adic properties of division polynomials and elliptic divisibility sequences." Mathematische Annalen, vol. 332, no. 2, 2004, pp. 443-471. |
Silverman, Joseph H. "The rank of elliptic surfaces in unramified abelian towers." Journal für die reine und angewandte Mathematik (Crelles Journal), vol. 2004, no. 577, 2004. |
Hoffstein, Jeffrey, Howgrave-Graham, Nick, Pipher, Jill, Silverman, Joseph H., Whyte, William. "NTRUSign: Digital Signatures Using the NTRU Lattice." Automata, Languages and Programming, 2003, pp. 122-140. |
Hoffstein, Jeffrey, Silverman, Joseph H. "Random small Hamming weight products with applications to cryptography." Discrete Applied Mathematics, vol. 130, no. 1, 2003, pp. 37-49. |
Howgrave-Graham, Nick, Nguyen, Phong Q., Pointcheval, David, Proos, John, Silverman, Joseph H., Singer, Ari, Whyte, William. "The Impact of Decryption Failures on the Security of NTRU Encryption." Automata, Languages and Programming, 2003, pp. 226-246. |
May, Alexander, Silverman, Joseph H. "Dimension Reduction Methods for Convolution Modular Lattices." Automata, Languages and Programming, 2001, pp. 110-125. |
Hoffstein, Jeffrey, Pipher, Jill, Silverman, Joseph H. "NSS: An NTRU Lattice-Based Signature Scheme." Automata, Languages and Programming, 2001, pp. 211-228. |
Bailey, Daniel V., Coffin, Daniel, Elbirt, Adam, Silverman, Joseph H., Woodbury, Adam D. "NTRU in Constrained Devices." Automata, Languages and Programming, 2001, pp. 262-272. |
Hindry, Marc, Silverman, Joseph H. "Diophantine Geometry." Graduate Texts in Mathematics, 2000. |
Bremner, A., Silverman, J.H., Tzanakis, N. "Integral Points in Arithmetic Progression on y2=x(x2−n2)." Journal of Number Theory, vol. 80, no. 2, 2000, pp. 187-208. |
Silverman, Joseph H. "On the distribution of integer points on curves of genus zero." Theoretical Computer Science, vol. 235, no. 1, 2000, pp. 163-170. |
Silverman, Joseph H. "Rings of Low Multiplicative Complexity." Finite Fields and Their Applications, vol. 6, no. 2, 2000, pp. 175-191. |
Silverman, Joseph H. "The xedni calculus and the elliptic curve discrete logarithm problem." Des. Codes Cryptogr., vol. 20, no. 1, 2000, pp. 5-40. |
Silverman, Joseph H., Bradley, David, Darling, Donald A. "A Zeta Function over a Recurrent Sequence: 10486." The American Mathematical Monthly, vol. 106, no. 7, 1999, pp. 686. |
Silverman, Joseph H. "Computing rational points on rank 1 elliptic curves via $L$-series and canonical heights." Mathematics of Computation, vol. 68, no. 226, 1999, pp. 835-859. |
Hindry, Marc, Silverman, Joseph. "Sur le nombre de points de torsion rationnels sur une courbe elliptique." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, vol. 329, no. 2, 1999, pp. 97-100. |
Silverman, Joseph H., Suzuki, Joe. "Elliptic Curve Discrete Logarithms and the Index Calculus." Automata, Languages and Programming, 1998, pp. 110-125. |
Hoffstein, Jeffrey, Pipher, Jill, Silverman, Joseph H. "NTRU: A ring-based public key cryptosystem." Automata, Languages and Programming, 1998, pp. 267-288. |
Rosen, Michael, Silverman, Joseph H. "On the rank of an elliptic surface." Inventiones Mathematicae, vol. 133, no. 1, 1998, pp. 43-67. |
Silverman, Joseph H. "The average rank of an algebraic family of elliptic curves." Journal für die reine und angewandte Mathematik (Crelles Journal), vol. 1998, no. 504, 1998. |
Silverman, Joseph H. "The space of rational maps on $mathbb{P}^1$." Duke Math. J., vol. 94, no. 1, 1998, pp. 41-77. |
Silverman, Joseph H. "Computing canonical heights with little (or no) factorization." Mathematics of Computation, vol. 66, no. 218, 1997, pp. 787-806. |
Call, Gregory S., Silverman, Joseph H. "Computing the canonical height on K3 surfaces." Mathematics of Computation, vol. 65, no. 213, 1996, pp. 259-291. |
Silverman, Joseph H. "Rational Functions with a Polynomial Iterate." Journal of Algebra, vol. 180, no. 1, 1996, pp. 102-110. |
Silverman, Joseph H. "Small Salem Numbers, Exceptional Units, and Lehmer's Conjecture." Rocky Mountain Journal of Mathematics, vol. 26, no. 3, 1996, pp. 1099-1114. |
Brumer, Armand, Silverman, Joseph H. "The number of elliptic curves over ℚ with conductorNwith conductorN." manuscripta mathematica, vol. 91, no. 1, 1996, pp. 95-102. |
MURTY, M. RAM, ROSEN, MICHAEL, SILVERMAN, JOSEPH H. "VARIATIONS ON A THEME OF ROMANOFF." Int. J. Math., vol. 07, no. 03, 1996, pp. 373-391. |
"Periodic points, multiplicities, and dynamical units." Journal für die reine und angewandte Mathematik (Crelles Journal), vol. 1995, no. 461, 1995. |
Silverman, Joseph H. "Advanced Topics in the Arithmetic of Elliptic Curves." Graduate Texts in Mathematics, 1994. |
Silverman, Joseph H. "Geometric and arithmetic properties of the Hénon map." Mathematische Zeitschrift, vol. 215, no. 1, 1994, pp. 237-250. |
Silverman, Joseph H. "Variation of the canonical height in algebraic families." Contemporary Mathematics, 1994, pp. 123-133. |
Silverman, J.H. "Variation of the Canonical Height On Elliptic Surfaces III: Global Boundedness Properties." Journal of Number Theory, vol. 48, no. 3, 1994, pp. 330-352. |
Silverman, J.H. "Variation of the Canonical Height On Elliptic-Surfaces II:." Journal of Number Theory, vol. 48, no. 3, 1994, pp. 291-329. |
Silverman, J. H. "A Uniform Bound for Rational Points on Twists of a Given Curve." Journal of the London Mathematical Society, vol. s2-47, no. 3, 1993, pp. 385-394. |
Silverman, Joseph H. "Integer points, Diophantine approximation, and iteration of rational maps." Duke Math. J., vol. 71, no. 3, 1993, pp. 793-829. |
Silverman, Joseph H. "Taxicabs and Sums of Two Cubes." The American Mathematical Monthly, vol. 100, no. 4, 1993, pp. 331. |
Silverman, Joseph H., Tate, John. "Rational Points on Elliptic Curves." Undergraduate Texts in Mathematics, 1992. |
"Variation of the canonical height on elliptic surfaces I: Three examples." Journal für die reine und angewandte Mathematik (Crelles Journal), vol. 1992, no. 426, 1992. |
Harris, Joe, Silverman, Joe. "Bielliptic curves and symmetric products." Proceedings of the American Mathematical Society, vol. 112, no. 2, 1991, pp. 347-347. |
Silverman, Joseph H. "Rational points on K3 surfaces: A new canonical height." Inventiones Mathematicae, vol. 105, no. 1, 1991, pp. 347-373. |
Silverman, Joseph H. "Rational Points on Symmetric Products of a Curve." American Journal of Mathematics, vol. 113, no. 3, 1991, pp. 471. |
Silverman, Joseph H. "Hecke points on modular curves." Duke Math. J., vol. 60, no. 2, 1990, pp. 401-423. |
Silverman, Joseph H. "Some arithmetic properties of Weierstrass points: Hyperelliptic curves." Boletim da Sociedade Brasileira de Matem�tica, vol. 21, no. 1, 1990, pp. 11-50. |
Silverman, Joseph H. "The difference between the Weil height and the canonical height on elliptic curves." Mathematics of Computation, vol. 55, no. 192, 1990, pp. 723-723. |
Silverman, Joseph H. "The Markoff equation X2 + Y2 + Z2 = aXYZ over quadratic imaginary fields." Journal of Number Theory, vol. 35, no. 1, 1990, pp. 72-104. |
Silverman, Joseph H. "Book Review: Introduction to Arakelov theory." Bulletin of the American Mathematical Society, vol. 21, no. 1, 1989, pp. 171-177. |
Silverman, Joseph H. "Elliptic curves of bounded degree and height." Proceedings of the American Mathematical Society, vol. 105, no. 3, 1989, pp. 540-540. |
Silverman, Joseph H. "Integral points on curves and surfaces." Number Theory, 1989, pp. 202-241. |
Silverman, Joseph H. "Computing heights on elliptic curves." Mathematics of Computation, vol. 51, no. 183, 1988, pp. 339-339. |
Hindry, M., Silverman, J. H. "The canonical height and integral points on elliptic curves." Inventiones Mathematicae, vol. 93, no. 2, 1988, pp. 419-450. |
Silverman, Joseph H. "Wieferich's criterion and the abc-conjecture." Journal of Number Theory, vol. 30, no. 2, 1988, pp. 226-237. |
"A quantitative version of Siegel's theorem: integral points on elliptic curves and Catalan curves." Journal für die reine und angewandte Mathematik (Crelles Journal), vol. 1987, no. 378, 1987. |
Silverman, Joseph H. "A survey of the theory of height functions." Contemporary Mathematics, 1987, pp. 269-278. |
Silverman, Joseph H. "Arithmetic distance functions and height functions in diophantine geometry." Mathematische Annalen, vol. 279, no. 2, 1987, pp. 193-216. |
Silverman, J. H. "Rational Points on Certain Families of Curves of Genus at Least 2." Proceedings of the London Mathematical Society, vol. s3-55, no. 3, 1987, pp. 465-481. |
Silverman, Joseph H. "Corrigendum to Integral points on Abelian varieties." Inventiones Mathematicae, vol. 84, no. 1, 1986, pp. 223-223. |
Silverman, Joseph H. "Points of Finite order on Elliptic Curves." The American Mathematical Monthly, vol. 93, no. 10, 1986, pp. 793. |
Silverman, Joseph H. "The Arithmetic of Elliptic Curves." Graduate Texts in Mathematics, 1986. |
Evertse, J.-H., Silverman, J. H. "Uniform bounds for the number of solutions to Yn = f( X)." Mathematical Proceedings of the Cambridge Philosophical Society, vol. 100, no. 02, 1986, pp. 237. |
Silverman, Joseph H. "Divisibility of the Specialization Map for Families of Elliptic Curves." American Journal of Mathematics, vol. 107, no. 3, 1985, pp. 555. |
Silverman, Joseph H. "Integral points on Abelian varieties." Inventiones Mathematicae, vol. 81, no. 2, 1985, pp. 341-346. |
Silverman, Joseph H. "An inequality relating the regulator and the discriminant of a number field." Journal of Number Theory, vol. 19, no. 3, 1984, pp. 437-442. |
Silverman, Joseph H. "Lower bounds for height functions." Duke Math. J., vol. 51, no. 2, 1984, pp. 395-403. |
Silverman, Joseph H. "The S-unit equation over function fields." Mathematical Proceedings of the Cambridge Philosophical Society, vol. 95, no. 01, 1984, pp. 3. |
Silverman, Joseph H. "Weierstrass equations and the minimal discriminant of an elliptic curve." Mathematika, vol. 31, no. 02, 1984, pp. 245. |
"Heights and the specialization map for families of abelian varieties." Journal für die reine und angewandte Mathematik (Crelles Journal), vol. 1983, no. 342, 1983. |
Silverman, J. H. "Integer Points on Curves of Genus 1." Journal of the London Mathematical Society, vol. s2-28, no. 1, 1983, pp. 1-7. |
Silverman, J. H. "Representations of integers by binary forms and the rank of the Mordell-Weil group." Inventiones Mathematicae, vol. 74, no. 2, 1983, pp. 281-292. |
Silverman, Joseph H. "The Neron fiber of abelian varieties with potential good reduction." Mathematische Annalen, vol. 264, no. 1, 1983, pp. 1-3. |
Silverman, Joseph H. "Integer points and the rank of Thue elliptic curves." Inventiones Mathematicae, vol. 66, no. 3, 1982, pp. 395-404. |
Silverman, Joseph H. "The Catalan equation over function fields." Trans. Amer. Math. Soc., vol. 273, no. 1, 1982, pp. 201-201. |
Simons Collaboration Grant for Mathematicians, 2012-2017
NSF EAGER Grant, 2014-2016
NSF Focused Research Grant, 2009-2012
NSF Research Grant, 2006-2008
NSA Research Grant, 2003-2006, "Investigation of Elliptic Curves and Moduli of Dynamical Systems"
NSF Research Grant, 1999-2003, "Arithmetic of Elliptic Curves"
NSF Research Grants, 1986-1998
Moduli Spaces and Arithmetic Dynamics (CRM Monograph Series, Vol. 30) American Mathematical Society, 2012.
Height estimates for equidimensional dominant rational maps, J. Ramanujan Math. Soc. 26 (2011), 145-163.
with Katherine Stange, Amicable pairs and aliquot cycles for elliptic curves, Exper. Math., 20(3) (2011), 329-357.
with Patrick Ingram, Primitive divisors in arithmetic dynamics, Proc. Camb. Philos. Soc. (2009), 146, #2, 289-302.
with Liang-Chung Hsia, On a dynamical Brauer-Manin obstruction, Proceedings of the Journees Arithmetiques 2007, J. Th\'eor. Nombres Bordeaux 21 (2009), 235-250.
with Jose Felipe Voloch, A Local-Global Criterion for Dynamics on P^1, Acta Arithmetica 137.3 (2009), 285-294.
Lifting and elliptic curve discrete logarithms, Selected Areas of Cryptography (SAC 2008), Lecture Notes in Computer Science 5381, Springer-Verlag, Berlin, 2009, 82-102.
with Jill Pipher and Jeffrey Hoffstein, An Introduction to Mathematical Cryptography, Undergraduate Texts in Mathematics, Springer-Verlag, 2008.
An Introduction to Mathematical Cryptography, Undergraduate Texts in Mathematics, Springer-Verlag, 2008.
Variation of periods modulo p in arithmetic dynamics, New York Journal of Math. 14 (2008), 601-616 (electronic).
The Arithmetic of Dynamical Systems, Graduate Texts in Math. 241, Springer-Verlag, N.Y., 2007.
with M. Rosen, On the independence of Heegner points associated to distinct quadratic imaginary fields, Journal of Number Theory 127 (2007), 10-36.
with S. Kawaguchi, Dynamics of projective morphisms having identical canonical heights, Proc. London Math. Soc. 95 (2007), 519-544.
Height bounds and preperiodic points for families of jointly regular affine mapsQuart. J. Pure Appl. Math. 2 (2006), 135-145.
p-adic properties of division polynomials and elliptic divisibility sequences, Mathematische Annalen 332 (2005), 443-471.
Generalized greatest common divisors, divisibility sequences, and Vojta's conjecture on blowups Monatsch. Math. 145 (2005), 333-350.
The rank of an elliptic surface over abelian unramified base extensions, J. Reine Angew. Math. 577 (2004), 153-169.
with Matthew Baker, A lower bound for the canonical height on abelian varieties over abelian extensions, Mathematical Research Letters 11 (2004), 377-396.
with J. Hoffstein, N. Howgrave-Graham, J. Pipher, W. Whyte, NTRUSign: Digital Signatures Using the NTRU Lattice, Topics in Cryptology - CT-RSA 2003, San Francisco, February 2003, Lecture Notes in Computer Science 2612, Springer-Verlag, Berlin, 2003, 122-140.
with N. Howgrave-Graham, P. Nguyen, D. Pointcheval, J. Proos, A. Singer, W. Whyte, The impact of decryption failure on the security of NTRU encryption, Advances in Cryptology -Crypto 2003, Lecture Notes in Computer Science 2729, Springer-Verlag, 2003.
Cryptography and Lattices Conference (CaLC 2001), Lecture Notes in Computer Science 2461, Springer-Verlag, 2001, 1-215.
with A. May, Dimension reduction methods for convolution modular lattices, Cryptography and Lattices Conference (CaLC 2001), Lecture Notes in Computer Science 2461, Springer-Verlag, 2001, 110-125.
with M. Hindry, Diophantine Geometry: An Introduction, Graduate Texts in Math. 201, Springer-Verlag, New York, 2000, 1-558.
with M. Hindry, Sur le nombre de points de torsion rationnels sur une courbe elliptique, C.R. Acad. Sci. Paris 329 (1999), 97--100.
with Jeffrey Hoffstein, Jill Pipher, NTRU: A Ring Based Public Key Cryptosystem, Algorithmic Number Theory (ANTS III), Portland, OR, June 1998, Lecture Notes in Computer Science 1423, Springer-Verlag, Berlin, 1998, 267-288.
with J. Suzuki, Elliptic curve discrete logarithms and the index calculus, Advances in Cryptology-AsiaCrypt 98, Beijing, October 1998, Lecture Notes in Computer Science 1514, Springer-Verlag, Berlin, 1998, 110-125.
with M. Rosen, On the rank of an elliptic surface, Invent. Math. 133 (1998), 43-67.
The space of rational maps on P1, Duke Math. J. 94 (1998), 41-77.
The average rank of an algebraic family of elliptic curves, J. Reine Angew. Math. 504 (1998), 227-236.
A Friendly Introduction to Number Theory, Prentice-Hall, N.J., 1997, 1-288; 2nd ed. 2001, 1-390; 3rd ed. 2005, 1-434.
On the field of definition for dynamical systems on P1, Compos. Math. 98 (1995), 269-304.
co-editor with G. Cornell and G. Stevens, Modular Forms and Fermat's Last Theorem, a conference held at Boston University, 1995, Springer-Verlag, N.Y., 1997, 1-569
with P. Morton, Periodic points, multiplicities, and dynamical units, J. Reine Angew. Math. 461 (1995), 81-122.
Advanced Topics in the Arithmetic of Elliptic Curves, Graduate Texts in Math. 151, Springer-Verlag, N.Y., 1994, 1-525.
Integer points, Diophantine approximation, and iteration of rational maps, Duke Math. J. 71 (1993), 793-829.
with G. Call, Canonical heights on varieties with morphisms, Compos. Math. 89 (1993), 163-205.
Variation of the canonical height on elliptic surfaces I: Three examples, J. Reine Angew. Math. 426 (1992), 151-178.
with J. Tate, Rational Points on Elliptic Curves, Undergraduate Texts in Math., Springer-Verlag, N.Y., 1992, 1-281.
with J.F. Voloch, Multiple Weierstrass points, Compos. Math. 79 (1991), 123-134.
Rational points on symmetric products of a curve, Am. J. Math. 113 (1991), 471-508.
Rational points on K3 surfaces: A new canonical height, Invent. Math. 105 (1991), 347-373.
Hecke points on modular curves, Duke Math. J. 60 (1990), 401-423.
with M. Hindry, The canonical height and integral points on elliptic curves, Invent. Math. 93 (1988), 419-450.
A quantitative version of Siegel's theorem: Integral points on elliptic curves and Catalan curves, J. Reine Angew. Math. 378 (1987), 60-100.
Integral points on abelian varieties are widely spaced, Compos. Math. 61 (1987), 253-266.
Arithmetic distance functions and height functions in Diophantine geometry Math. Ann., 279 (1987), 193-216.
The Arithmetic of Elliptic Curves, Graduate Texts in Math. 106 , Springer-Verlag, N.Y., 1986, 1-400
Integral points on abelian varieties, Invent. Math. 81 (1985), 341-346.
Divisibility of the specialization map for families of elliptic curves, Amer. J. Math. 107 (1985), 555-565.
Lower bounds for height functions, Duke Math. J. 51 (1984), 395-403.
co-editor with G. Cornell, Arithmetic Geometry, a conference held at Storrs, Connecticut, 1984, Springer-Verlag, N.Y., 1986, 1-353
Representations of integers by binary forms and the rank of the Mordell-Weil group, Invent. Math. 74 (1983), 281-292.
Heights and the specialization map for families of abelian varieties, J. Reine Angew. Math. 342 (1983), 197-211.
Integer points and the rank of Thue elliptic curves, Invent. Math. 66 (1982), 395-404.
Lower bound for the canonical height on elliptic curves, Duke Math. J. 48 (1981), 633-648.
Year | Degree | Institution |
---|---|---|
1982 | PhD | Harvard University |
1979 | MA | Harvard University |
1977 | BS | Brown University |
Name | Title |
---|---|
Hoffstein, Jeffrey | Professor of Mathematics, Chair of Mathematics |
Pipher, Jill | Elisha Benjamin Andrews Professor of Mathematics, Vice President for Research |
MATH 0420 - Introduction to Number Theory |
MATH 0540 - Honors Linear Algebra |
MATH 0750 - Introduction to Higher Mathematics |
MATH 0760 - Introduction to Higher Mathematics |
MATH 1530 - Abstract Algebra |
MATH 1580 - Cryptography |
MATH 2530 - Number Theory |
MATH 2540 - Number Theory |