Jeffrey Ezra Hoffstein (born September 28, 1953 in

New York City New York, often called New York City (NYC), is the most populous city in the United States, located at the southern tip of New York State on one of the world's largest natural harbors. The city comprises five boroughs, each coextensive w ...

) is an American mathematician, specializing in number theory, automorphic forms, and cryptography.

Education and career

Hoffstein graduated with a bachelor's degree in 1974 from

Cornell University Cornell University is a Private university, private Ivy League research university based in Ithaca, New York, United States. The university was co-founded by American philanthropist Ezra Cornell and historian and educator Andrew Dickson W ...

. He received his Ph.D. in 1978 from

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...

with thesis ''Class numbers of totally complex quadratic extensions of totally real fields'' under the supervision of

Harold Stark Harold Mead Stark (born August 6, 1939) is an Americans, American mathematician, specializing in number theory. He is best known for his solution of the Carl Friedrich Gauss, Gauss class number 1 problem, in effect Stark–Heegner theorem, corre ...

. Hoffstein was a postdoc at the

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

and then at the

University of Cambridge The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...

. From 1980 to 1982 he was an assistant professor at

Brown University Brown University is a Private university, private Ivy League research university in Providence, Rhode Island, United States. It is the List of colonial colleges, seventh-oldest institution of higher education in the US, founded in 1764 as the ' ...

. From 1982 he was an assistant professor and then an associate professor at the

University of Rochester The University of Rochester is a private university, private research university in Rochester, New York, United States. It was founded in 1850 and moved into its current campus, next to the Genesee River in 1930. With approximately 30,000 full ...

. Since 1989 he is a full professor at Brown University and he was the chair of the mathematics department from 2009 to 2013 and again from 2019 to 2024. His research uses analytic and algebraic methods to investigate L-series of automorphic forms over GL(n) and number fields. With co-workers he has developed new techniques for Dirichlet series in several complex variables. He was several times a visiting scholar at the Institute for Advanced Study (1978/79, 1985, 1986/87). At MSRI, in the academic year 1994/95 he initiated seminars on automorphic functions. In 1984 he was a Fulbright Fellow. He was a visiting professor at the University of Texas at Austin in the spring of 1984 and at the

University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen (, commonly referred to as Georgia Augusta), is a Public university, public research university in the city of Göttingen, Lower Saxony, Germany. Founded in 1734 ...

in the fall of 1986. He became a Fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

in the class of 2019. In 1996, Hoffstein, along with

Jill Pipher Jill Catherine Pipher (born December 14, 1955, in Harrisburg, Pennsylvania) is an American mathematician. She served as president of the American Mathematical Society (AMS, 2019–2020). and president of the Association for Women in Mathematics ( ...

Joseph Silverman Joseph Silverman (August 25, 1860 in Ohio – July 26, 1930 in New York City), was a leading American Reform rabbi and author. He was the first American born rabbi to serve in New York City. Born in Cincinnati, he attended the University of ...

, and Daniel Liemann (Hoffstein's former doctoral student), founded NTRU Cryptosystems, Inc. to market their cryptographic algorithms,

NTRUEncrypt The NTRUEncrypt public key cryptosystem, also known as the NTRU encryption algorithm, is an NTRU lattice-based cryptography, lattice-based alternative to RSA (algorithm), RSA and elliptic curve cryptography (ECC) and is based on the lattice proble ...

and

NTRUSign NTRUSign, also known as the NTRU Signature Algorithm, is an NTRU public-key cryptography digital signature algorithm based on the GGH signature scheme. The original version of NTRUSign was Polynomial Authentication and Signature Scheme (PASS), a ...

. NTRU Cryptosystems was acquired by Security Innovation in 2009.

Selected publications

* with Jill Pipher, Joseph Silverman: ''An Introduction to Mathematical Cryptography''. Springer-Verlag, 2008
2014, 2nd edition
* Some analytic bounds for zeta functions and class numbers,

Inventiones Mathematicae ''Inventiones Mathematicae'' is a mathematical journal published monthly by Springer Science+Business Media. It was established in 1966 and is regarded as one of the most prestigious mathematics journals in the world. The current (2023) managing ...

, vol. 55, 1979, pp. 37–47 * with

Dorian Goldfeld Dorian Morris Goldfeld (born January 21, 1947) is an American mathematician working in analytic number theory and automorphic forms at Columbia University. Professional career Goldfeld received his B.S. degree in 1967 from Columbia University. H ...

: Eisenstein series of half integral weight and the mean value of real Dirichlet L-series, Inv. Math., vol. 80, 1985, pp. 185–208 * with

Daniel Bump Daniel Willis Bump (born 13 May 1952) is a mathematician who is a professor at Stanford University working in representation theory. He is a fellow of the American Mathematical Society since 2015, for "contributions to number theory, representation ...

, Solomon Friedberg: ''On some applications of automorphic forms to number theory'', Bulletin AMS, Band 33, 1996, pp. 157–175, * with Bump ''Cubic metaplectic forms on GL(3)'', Inv. Math., 84, 1986, pp. 481–505 * with Bump, D. Ginzburg ''The symmetric cube'', Inv. Math., 125, 1996, pp. 413–449 * with Bump, Friedberg ''Eisenstein series on the metaplectic group and non vanishing theorems for automorphic L-functions and their derivatives'',

Annals of Mathematics The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as t ...

, vol. 131, 1990, pp. 53–127 * with Bump, Friedberg ''Nonvanishing theorems for L-functions of modular forms and their derivatives'', Inv. Math., 102, 1990, 543–618 * with Friedberg ''Nonvanishing theorems for automorphic L-functions on GL(2)'', Annals of Mathematics, vol. 142, 1995, pp. 385–423 * with P. Lockhart ''Coefficients of Maass forms and the Siegel zero'', Annals of Mathematics, vol. 140, 1994, pp. 161–181

References

External links

* {{DEFAULTSORT:Hoffstein, Jeffrey 1953 births Living people 20th-century American mathematicians 21st-century American mathematicians American number theorists Cornell University alumni Massachusetts Institute of Technology alumni University of Rochester faculty Brown University faculty Fellows of the American Mathematical Society