Samuel James Patterson

Samuel James Patterson (September 7, 1948 in Belfast)Author Profile: Samuel James Patterson
in zbMATH database is a Northern Irish mathematician specializing in analytic number theory. He has been a professor at the University of Göttingen since 1981.Literature by and about Samuel J. Patterson
in the German National Library catalogue

Biography

Patterson was born in Belfast and grew up in the east of the city, attending Grosvenor High School. He went to Clare College, Cambridge, in 1967, and received his BA in mathematics in 1970, and his Ph.D. (completed in 1974, awarded in 1975) on "The limit set of a Fuchsian group" under Alan Beardon. He spent 1974–1975 at Göttingen, 1975–1979 he was back at Cambridge, and 1979–1981 he was at Harvard as Benjamin Pierce Lecturer. From 1981 to his retirement in 2011 he was professor of mathematics at Göttingen.

His 18 PhD students include Jörg Brüdern and Bernd Otto Stratmann.Samuel James Patterson
at the Mathematics Genealogy Project

He is the brother of the Northern Irish taxonomist David Joseph Patterson.

Mathematics

Subjects that Patterson deals with include discontinuous groups ( Fuchsian groups), different zeta functions (for example those of Ruelle and Selberg, in particular those associated with certain groups of infinite covolume), metaplectic groups, generalized theta functions, and exponential sums in analytical number theory.

In 1978, together with Roger Heath-Brown, he disproved the Kummer conjecture on cubic Gauss sums.

He proposed a new conjecture which was based on insights from his determination of the coefficients of the cuspidal Fourier expansions of the metaplectic cubic theta function. This revised conjecture remained open until 2021, when it was finally proved by Alexander Dunn and Maksym Radziwiłł at Caltech.

In 1976 Patterson introduced what later became known as the Patterson-Sullivan measure. The concept was further developed and extended by Dennis Sullivan starting in 1979. It has proved to be a useful tool in studying Fuchsian and Kleinian groups (and certain generalizations) and their limit sets.

History of mathematics

Patterson is also interested in the history of mathematics. For example, together with Ralf Meyer, he contributed an updated introduction to a new edition of a classic textbook by Hermann Weyl, and an introduction to the classic textbook of Whittaker and Watson. He has collaborated with Norbert Schappacher on elucidating the biography of Kurt Heegner.

Honors and awards

In 1984 Patterson received the Whitehead Prize of the London Mathematical Society. He is on the Executive Committee of the Leibniz Archives based in Hannover and has been a member of the Göttingen Academy of Sciences since 1998. From 1982 to 1994 he was an editor of Crelle's Journal.

To mark his 60th birthday friends and colleagues in Göttingen organized a three day conference to celebrate his life in July, 2009.International Conference on the Occasion of the 60th Birthday of Samuel J. Patterson
Göttingen, July 27–29, 2009 Speakers at this gathering included Daniel Bump, Dorian Goldfeld,
David Kazhdan, and Andrew Ranicki.Mathematics: International Conference on Questions of Number Theory
University of Göttingen A commemorative volume, ''Contributions in Analytic and Algebraic Number Theory'' (Springer 2012), edited by Valentin Blomer & Preda Mihăilescu, collecting articles related to or developed at the conference, was issued as a Festschrift for him.Festschrift for S. J. Patterson
The text that comprises this volume is a collection of surveys and original works from experts in the fields of algebraic number theory, analytic number theory, harmonic analysis, and hyperbolic geometry. A portion of the collected contributions have been developed from lectures given at the "International Conference on the Occasion of the 60th Birthday of S. J. Patterson"

Selected papers

* ′A lattice-point problem in hyperbolic space′, Mathematika, 22, 81-88 (1975). DOI: 10.1112/S0025579300004526
* ′The limit set of a Fuchsian group′, Acta Math. 136, 241-273 (1976) DOI: 10.1007/BF02392046
* ′The Laplacian operator on a Riemann surface′, Compos. Math. 31, 83-107 (1975) Compos. Math. 32, 71-112 (1976) Compos. Math. 33, 227-259 (1976)
* ′A cubic analogue of the theta series′, J. Reine Angew. Math. 296, 125-161 (1977). J. Reine Angew. Math. 296, 217-220 (1977) DOI: 10.1515/crll.1977.296.125, 10.1515/crll.1977.296.217
* ′On the distribution of Kummer sums′, J. Reine Angew. Math. 303/304, 126-143 (1978). DOI: 10.1515/crll.1978.303-304.126
* (With D.R. Heath-Brown)′ The distribution of Kummer sums at prime arguments′, J. Reine Angew. Math. 310, 111-130 (1979).
* (With D.A. Kazhdan)′ Metaplectic forms′, Publ. Math., Inst. Hautes Étud. Sci. 59, 35-142 (1984) + 62, 149(1985) DOI: 10.1007/BF02698770, 10.1007/BF02698809
* ′The Hardy-Littlewood method and Diophantine analysis in the light of Igusa'a Work′, Mathematica Goettingensis (1985-11,45pp)
* ′The Selberg zeta-function of a Kleinian group. Number theory, trace formulas and discrete groups′, Symp. in Honor of Atle Selberg, Oslo/Norway 1987, 409-441 (1989)
* (With P.A. Perry) ppendix by Charles Epstein′The divisor of Selberg’s zeta function for Kleinian groups′, Duke Math. J. 106, No. 2, 321-390 (2001) DOI: 10.1215/S0012-7094-01-10624-8
* (With R. Livné) ′The first moment of cubic exponential sums′, Invent. Math. 148, No. 1, 79-116 (2002) DOI: 10.1007/s002220100189

References

External links

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{{DEFAULTSORT:Patterson, Samuel James
Scientists from Belfast
1948 births
Living people
Number theorists
20th-century Irish mathematicians
21st-century Irish mathematicians
Academic staff of the University of Göttingen
Whitehead Prize winners