Samuel James Patterson

Samuel James Patterson (September 7, 1948 in Belfast)[2] is a Northern Irish mathematician specializing in analytic number theory. He has been a professor at the University of Göttingen since 1981.[3]

Samuel James Patterson
Samuel Patterson (2nd from right) 2004 in Oberwolfach, with (from left) Martin Huxley, Yōichi Motohashi, Matti Jutila
Born (1948-09-07) September 7, 1948
Belfast
Alma materCambridge University (PhD)
Known forDisproving The Kummer conjecture on cubic Gauss sums
AwardsWhitehead Prize (1984)
Scientific career
Fieldsanalytic number theory
InstitutionsUniversity of Göttingen
ThesisThe Limit Set of a Fuchsian Group (1975)
Doctoral advisorAlan Beardon[1]
WebsiteUniversity of Göttingen: Samuel J. Patterson

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.[4] 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.

He wrote the book An Introduction to the Riemann Zeta Function (Cambridge, 1988).

Subjects that Patterson deals with include discontinuous groups (Fuchsian groups), different zeta functions (for example those of Ruelle and Selberg), metaplectic groups, generalized theta functions, and exponential sums in analytical number theory. He 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.[5]

In 1978, together with Roger Heath-Brown, he disproved the Kummer conjecture on cubic Gauss sums.[6][7]

His 17 PhD students include Jörg Brüdern and Bernd Otto Stratmann.

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

Honors and awards

In 1984 Patterson received the Whitehead Prize of the London Mathematical Society.[8] He is on the Executive Committee of the Leibniz Archives based in Hannover[9] and a member of the Göttingen Academy of Sciences (1998).[10] From 1982 to 1994 he was an editor of Crelle's Journal.[11]

To mark his 60th birthday friends and colleagues in Göttingen organized a three day conference to celebrate his life in July, 2009.[12] Speakers at this gathering included Daniel Bump, Dorian Goldfeld, David Kazhdan, and Andrew Ranicki[13] 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.[14]

Papers
  • 1989: On Ruelle's zeta function, Sonderforschungsbereiche Geometry and Analysis[15]
  • 1988: Introduction to the theory of the Riemann Zeta Function, Cambridge University Press
  • 1987: The symmetric square L-function attached to a cuspidal automorphic representation of GL3, Sonderforschungsbereich
  • 1986: The Selberg zeta function of a Kleinian group, Sonderforschungsbereich
  • 1985: The distribution of general Gauss sums and similar arithmetic functions at prime arguments, Sonderforschungsbereich
  • 1985: The Hardy-Littlewood method and diophantine analysis in the light of Igusa's work, Sonderforschungsbereich
  • 1985: Tori in metaplectic covers of Gl2 and applications to a formula of Loxton–-Matthews, Sonderforschungsbereich
  • 1985: Metaplectic forms and Gauss sums, Sonderforschungsbereich
  • 1976: The limit set of a Fuchsian group, Acta Math. 136 (1976), 241–273. doi:10.1007/BF02392046[1]

References
  1. Samuel James Patterson at the Mathematics Genealogy Project
  2. Author Profile: Samuel James Patterson in zbMATH database
  3. Literature by and about Samuel J. Patterson in the German National Library catalogue
  4. The limit set of a Fuchsian group by S. J. Patterson, Acta Math., Volume 136 (1976), 241–273.
  5. Moulton, F. R. (1914). "Review: Die Idee der Riemannschen Fläche by Hermann Weyl" (PDF). Bull. Amer. Math. Soc. 20 (7): 384–387. doi:10.1090/s0002-9904-1914-02505-4.
  6. Heath-Brown, D. Roger; Patterson, Samuel James (1979). "The distribution of Kummer sums at prime arguments". J. Reine Angew. Math. 1979 (310): 111–130. doi:10.1515/crll.1979.310.111. MR 0546667.
  7. Heath-Brown, D. R. (2000). "Kummer's conjecture for cubic Gauss sums" (PDF). Israel J. Math. 120: part A, 97–124. doi:10.1007/s11856-000-1273-y. MR 1815372.
  8. List of LMS prize winners The London Mathematical Society
  9. Leibniz-Archiv/Leibniz Research Center Hannover
  10. Göttingen Academy of Sciences: members
  11. Journal für die reine und angewandte Mathematik (Crelles Journal) Band 737, April 2018
  12. International Conference on the Occasion of the 60th Birthday of Samuel J. Patterson Göttingen, July 27–29, 2009
  13. Mathematics: International Conference on Questions of Number Theory University of Göttingen
  14. 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"
  15. Catalog of the German National Library: Papers of Samual J. Patterson
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