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/Journal of Number Theory. 2019; 195 : 1-22. |
Silverman, Joseph H., Call, Gregory S. Degeneration of dynamical degrees in families of maps. Acta Arithmetica/Acta Arithmetica. 2018; 184 (2) : 101-116. |
Silverman, Joseph Good reduction and Shafarevich-type theorems for dynamical systems with portrait level structures. Pacific Journal of Mathematics/Pacific Journal of Mathematics. 2018; 295 (1) : 145-190. |
Silverman, Joseph H. Divisor divisibility sequences on tori. Acta Arithmetica/Acta Arithmetica. 2017; 177 (4) : 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/Mathematical Research Letters. 2017; 24 (6) : 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/Bulletin of the American Mathematical Society. 2017; 54 (4) : 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). 2016; 2016 (713) |
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.. 2015; 368 (7) : 5009-5035. |
Kawaguchi, Shu, Silverman, Joseph H. Examples of dynamical degree equals arithmetic degree. Michigan Math. J.. 2014; 63 (1) : 41-63. |
Hoffstein, Jeff, Pipher, Jill, Schanck, John M., Silverman, Joseph H., Whyte, William Transcript Secure Signatures Based on Modular Lattices. Post-Quantum Cryptography/Automata, Languages and Programming. 2014; : 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. 2013; 20 (3) : 547-566. |
Silverman, Joseph H. Primitive divisors, dynamical Zsigmondy sets, and Vojtaʼs conjecture. Journal of Number Theory. 2013; 133 (9) : 2948-2963. |
Silverman, Joseph H. WHAT IS...the p-adic Mandelbrot Set?. Notices Amer. Math. Soc.. 2013; 60 (08) : 1. |
INGRAM, PATRICK, MAHÉ, VALÉRY, SILVERMAN, JOSEPH H., STANGE, KATHERINE E., STRENG, MARCO ALGEBRAIC DIVISIBILITY SEQUENCES OVER FUNCTION FIELDS. J. Aust. Math. Soc.. 2012; 92 (01) : 99-126. |
Silverman, Joseph H. An algebraic approach to certain cases of Thurston rigidity. Proceedings of the American Mathematical Society. 2012; 140 (10) : 3421-3434. |
Silverman, Joseph H. Book Review: Some problems of unlikely intersections in arithmetic and geometry. Bulletin of the American Mathematical Society. 2012; 50 (2) : 353-358. |
SILVERMAN, JOSEPH H. Dynamical degree, arithmetic entropy, and canonical heights for dominant rational self-maps of projective space. Ergod. Th. Dynam. Sys.. 2012; 34 (02) : 633-664. |
Silverman, Joseph H. Elliptic Carmichael numbers and elliptic Korselt criteria. Acta Arithmetica. 2012; 155 (3) : 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. 2012; 24 (3) : 751-772. |
Hsia, Liang-Chung, Silverman, Joseph A quantitative estimate for quasiintegral points in orbits. Pacific Journal of Mathematics. 2011; 249 (2) : 321-342. |
Silverman, Joseph H., Stange, Katherine E. Amicable Pairs and Aliquot Cycles for Elliptic Curves. Experimental Mathematics. 2011; 20 (3) : 329-357. |
Silverman, Joseph H., Stange, Katherine E. Terms in elliptic divisibility sequences divisible by their indices. Acta Arithmetica. 2011; 146 (4) : 355-378. |
Silverman, Joseph H. A Survey of Local and Global Pairings on Elliptic Curves and Abelian Varieties. Automata, Languages and Programming. 2010; : 377-396. |
Silverman, Joseph Local-global aspects of (hyper)elliptic curves over (in)finite fields. Advances in Mathematics of Communications. 2010; 4 (2) : 101-114. |
Kawaguchi, Shu, Silverman, Joseph H. Canonical Heights and the Arithmetic Complexity of Morphisms on Projective Space. Pure and Applied Mathematics Quarterly. 2009; 5 (4) : 1201-1217. |
Silverman, Joseph H. Lifting and Elliptic Curve Discrete Logarithms. Automata, Languages and Programming. 2009; : 82-102. |
Silverman, Joseph H., Voloch, José Felipe Mathematische Annalen. Acta Arithmetica. 2009; 137 (3) : 285-294. |
Hsia, Liang-Chung, Silverman, Joseph On a dynamical Brauer–Manin obstruction. J. Théor. Nombres Bordeaux. 2009; 21 (1) : 235-250. |
Kawaguchi, Shu, Silverman, Joseph H. Nonarchimedean Green functions and dynamics on projective space. Mathematische Zeitschrift. 2008; 262 (1) : 173-197. |
INGRAM, PATRICK, SILVERMAN, JOSEPH H. Primitive divisors in arithmetic dynamics. Math. Proc. Camb. Phil. Soc.. 2008; 146 (02) : 289. |
Kawaguchi, S., Silverman, J. H. Dynamics of projective morphisms having identical canonical heights. Proceedings of the London Mathematical Society. 2007; 95 (2) : 519-544. |
Rosen, Michael, Silverman, Joseph H. On the independence of Heegner points associated to distinct quadratic imaginary fields. Journal of Number Theory. 2007; 127 (1) : 10-36. |
Silverman, Joseph H. Height Bounds and Preperiodic Points for Families of Jointly Regular Affine Maps. Pure and Applied Mathematics Quarterly. 2006; 2 (1) : 135-145. |
Silverman, Joseph H., Whyte, William Timing Attacks on NTRUEncrypt Via Variation in the Number of Hash Calls. Automata, Languages and Programming. 2006; : 208-224. |
Silverman, Joseph H. Addendum to “p-adic properties of division polynomials and elliptic divisibility sequences”. Mathematische Annalen. 2005; 332 (2) : 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; : 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; : 118-135. |
Silverman, Joseph H. Generalized Greatest Common Divisors, Divisibility Sequences, and Vojta’s Conjecture for Blowups. Mh Math. 2005; 145 (4) : 333-350. |
Baker, Matthew H., Silverman, Joseph H. A lower bound for the canonical height on abelian varieties over abelian extensions. Mathematical Research Letters. 2004; 11 (3) : 377-396. |
Silverman, Joseph H. A lower bound for the canonical height on elliptic curves over abelian extensions. Journal of Number Theory. 2004; 104 (2) : 353-372. |
Silverman, Joseph H. Common divisors of elliptic divisibility sequences over function fields. manuscripta mathematica. 2004; 114 (4) |
Silverman, Joseph H. p-adic properties of division polynomials and elliptic divisibility sequences. Mathematische Annalen. 2004; 332 (2) : 443-471. |
Silverman, Joseph H. The rank of elliptic surfaces in unramified abelian towers. Journal für die reine und angewandte Mathematik (Crelles Journal). 2004; 2004 (577) |
Hoffstein, Jeffrey, Howgrave-Graham, Nick, Pipher, Jill, Silverman, Joseph H., Whyte, William NTRUSign: Digital Signatures Using the NTRU Lattice. Automata, Languages and Programming. 2003; : 122-140. |
Hoffstein, Jeffrey, Silverman, Joseph H. Random small Hamming weight products with applications to cryptography. Discrete Applied Mathematics. 2003; 130 (1) : 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; : 226-246. |
May, Alexander, Silverman, Joseph H. Dimension Reduction Methods for Convolution Modular Lattices. Automata, Languages and Programming. 2001; : 110-125. |
Hoffstein, Jeffrey, Pipher, Jill, Silverman, Joseph H. NSS: An NTRU Lattice-Based Signature Scheme. Automata, Languages and Programming. 2001; : 211-228. |
Bailey, Daniel V., Coffin, Daniel, Elbirt, Adam, Silverman, Joseph H., Woodbury, Adam D. NTRU in Constrained Devices. Automata, Languages and Programming. 2001; : 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. 2000; 80 (2) : 187-208. |
Silverman, Joseph H. On the distribution of integer points on curves of genus zero. Theoretical Computer Science. 2000; 235 (1) : 163-170. |
Silverman, Joseph H. Rings of Low Multiplicative Complexity. Finite Fields and Their Applications. 2000; 6 (2) : 175-191. |
Silverman, Joseph H. The xedni calculus and the elliptic curve discrete logarithm problem. Des. Codes Cryptogr.. 2000; 20 (1) : 5-40. |
Silverman, Joseph H., Bradley, David, Darling, Donald A. A Zeta Function over a Recurrent Sequence: 10486. The American Mathematical Monthly. 1999; 106 (7) : 686. |
Silverman, Joseph H. Computing rational points on rank 1 elliptic curves via $L$-series and canonical heights. Mathematics of Computation. 1999; 68 (226) : 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. 1999; 329 (2) : 97-100. |
Silverman, Joseph H., Suzuki, Joe Elliptic Curve Discrete Logarithms and the Index Calculus. Automata, Languages and Programming. 1998; : 110-125. |
Hoffstein, Jeffrey, Pipher, Jill, Silverman, Joseph H. NTRU: A ring-based public key cryptosystem. Automata, Languages and Programming. 1998; : 267-288. |
Rosen, Michael, Silverman, Joseph H. On the rank of an elliptic surface. Inventiones Mathematicae. 1998; 133 (1) : 43-67. |
Silverman, Joseph H. The average rank of an algebraic family of elliptic curves. Journal für die reine und angewandte Mathematik (Crelles Journal). 1998; 1998 (504) |
Silverman, Joseph H. The space of rational maps on $mathbb{P}^1$. Duke Math. J.. 1998; 94 (1) : 41-77. |
Silverman, Joseph H. Computing canonical heights with little (or no) factorization. Mathematics of Computation. 1997; 66 (218) : 787-806. |
Call, Gregory S., Silverman, Joseph H. Computing the canonical height on K3 surfaces. Mathematics of Computation. 1996; 65 (213) : 259-291. |
Silverman, Joseph H. Rational Functions with a Polynomial Iterate. Journal of Algebra. 1996; 180 (1) : 102-110. |
Silverman, Joseph H. Small Salem Numbers, Exceptional Units, and Lehmer's Conjecture. Rocky Mountain Journal of Mathematics. 1996; 26 (3) : 1099-1114. |
Brumer, Armand, Silverman, Joseph H. The number of elliptic curves over ℚ with conductorNwith conductorN. manuscripta mathematica. 1996; 91 (1) : 95-102. |
MURTY, M. RAM, ROSEN, MICHAEL, SILVERMAN, JOSEPH H. VARIATIONS ON A THEME OF ROMANOFF. Int. J. Math.. 1996; 07 (03) : 373-391. |
Periodic points, multiplicities, and dynamical units.. Journal für die reine und angewandte Mathematik (Crelles Journal). 1995; 1995 (461) |
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. 1994; 215 (1) : 237-250. |
Silverman, Joseph H. Variation of the canonical height in algebraic families. Contemporary Mathematics. 1994; : 123-133. |
Silverman, J.H. Variation of the Canonical Height On Elliptic Surfaces III: Global Boundedness Properties. Journal of Number Theory. 1994; 48 (3) : 330-352. |
Silverman, J.H. Variation of the Canonical Height On Elliptic-Surfaces II:. Journal of Number Theory. 1994; 48 (3) : 291-329. |
Silverman, J. H. A Uniform Bound for Rational Points on Twists of a Given Curve. Journal of the London Mathematical Society. 1993; s2-47 (3) : 385-394. |
Silverman, Joseph H. Integer points, Diophantine approximation, and iteration of rational maps. Duke Math. J.. 1993; 71 (3) : 793-829. |
Silverman, Joseph H. Taxicabs and Sums of Two Cubes. The American Mathematical Monthly. 1993; 100 (4) : 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). 1992; 1992 (426) |
Harris, Joe, Silverman, Joe Bielliptic curves and symmetric products. Proceedings of the American Mathematical Society. 1991; 112 (2) : 347-347. |
Silverman, Joseph H. Rational points on K3 surfaces: A new canonical height. Inventiones Mathematicae. 1991; 105 (1) : 347-373. |
Silverman, Joseph H. Rational Points on Symmetric Products of a Curve. American Journal of Mathematics. 1991; 113 (3) : 471. |
Silverman, Joseph H. Hecke points on modular curves. Duke Math. J.. 1990; 60 (2) : 401-423. |
Silverman, Joseph H. Some arithmetic properties of Weierstrass points: Hyperelliptic curves. Boletim da Sociedade Brasileira de Matem�tica. 1990; 21 (1) : 11-50. |
Silverman, Joseph H. The difference between the Weil height and the canonical height on elliptic curves. Mathematics of Computation. 1990; 55 (192) : 723-723. |
Silverman, Joseph H. The Markoff equation X2 + Y2 + Z2 = aXYZ over quadratic imaginary fields. Journal of Number Theory. 1990; 35 (1) : 72-104. |
Silverman, Joseph H. Book Review: Introduction to Arakelov theory. Bulletin of the American Mathematical Society. 1989; 21 (1) : 171-177. |
Silverman, Joseph H. Elliptic curves of bounded degree and height. Proceedings of the American Mathematical Society. 1989; 105 (3) : 540-540. |
Silverman, Joseph H. Integral points on curves and surfaces. Number Theory. 1989; : 202-241. |
Silverman, Joseph H. Computing heights on elliptic curves. Mathematics of Computation. 1988; 51 (183) : 339-339. |
Hindry, M., Silverman, J. H. The canonical height and integral points on elliptic curves. Inventiones Mathematicae. 1988; 93 (2) : 419-450. |
Silverman, Joseph H. Wieferich's criterion and the abc-conjecture. Journal of Number Theory. 1988; 30 (2) : 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). 1987; 1987 (378) |
Silverman, Joseph H. A survey of the theory of height functions. Contemporary Mathematics. 1987; : 269-278. |
Silverman, Joseph H. Arithmetic distance functions and height functions in diophantine geometry. Mathematische Annalen. 1987; 279 (2) : 193-216. |
Silverman, J. H. Rational Points on Certain Families of Curves of Genus at Least 2. Proceedings of the London Mathematical Society. 1987; s3-55 (3) : 465-481. |
Silverman, Joseph H. Corrigendum to Integral points on Abelian varieties. Inventiones Mathematicae. 1986; 84 (1) : 223-223. |
Silverman, Joseph H. Points of Finite order on Elliptic Curves. The American Mathematical Monthly. 1986; 93 (10) : 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). Math. Proc. Camb. Phil. Soc.. 1986; 100 (02) : 237. |
Silverman, Joseph H. Divisibility of the Specialization Map for Families of Elliptic Curves. American Journal of Mathematics. 1985; 107 (3) : 555. |
Silverman, Joseph H. Integral points on Abelian varieties. Inventiones Mathematicae. 1985; 81 (2) : 341-346. |
Silverman, Joseph H. An inequality relating the regulator and the discriminant of a number field. Journal of Number Theory. 1984; 19 (3) : 437-442. |
Silverman, Joseph H. Lower bounds for height functions. Duke Math. J.. 1984; 51 (2) : 395-403. |
Silverman, Joseph H. The S-unit equation over function fields. Math. Proc. Camb. Phil. Soc.. 1984; 95 (01) : 3. |
Silverman, Joseph H. Weierstrass equations and the minimal discriminant of an elliptic curve. Mathematika. 1984; 31 (02) : 245. |
Heights and the specialization map for families of abelian varieties.. Journal für die reine und angewandte Mathematik (Crelles Journal). 1983; 1983 (342) |
Silverman, J. H. Integer Points on Curves of Genus 1. Journal of the London Mathematical Society. 1983; s2-28 (1) : 1-7. |
Silverman, J. H. Representations of integers by binary forms and the rank of the Mordell-Weil group. Inventiones Mathematicae. 1983; 74 (2) : 281-292. |
Silverman, Joseph H. The Neron fiber of abelian varieties with potential good reduction. Mathematische Annalen. 1983; 264 (1) : 1-3. |
Silverman, Joseph H. Integer points and the rank of Thue elliptic curves. Inventiones Mathematicae. 1982; 66 (3) : 395-404. |
Silverman, Joseph H. The Catalan equation over function fields. Trans. Amer. Math. Soc.. 1982; 273 (1) : 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 |
Pipher, Jill | Vice President for Research, Elisha Benjamin Andrews Professor of Mathematics |
MATH 0420 - Introduction to Number Theory |
MATH 0750 - Introduction to Higher Mathematics |
MATH 0760 - Introduction to Higher Mathematics |
MATH 1580 - Cryptography |
MATH 2530 - Number Theory |
MATH 2540 - Number Theory |
MATH 2710E - Arithmetic Groups |