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Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

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On some applications of automorphic forms to number theory
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by Daniel Bump, Solomon Friedberg and Jeffrey Hoffstein PDF
Bull. Amer. Math. Soc. 33 (1996), 157-175 Request permission

Abstract:

A basic idea of Dirichlet is to study a collection of interesting quantities $\{a_n\}_{n\geq 1}$ by means of its Dirichlet series in a complex variable $w$: $\sum _{n\geq 1}a_nn^{-w}$. In this paper we examine this construction when the quantities $a_n$ are themselves infinite series in a second complex variable $s$, arising from number theory or representation theory. We survey a body of recent work on such series and present a new conjecture concerning them.
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Additional Information
  • Daniel Bump
  • Affiliation: Department of Mathematics, Stanford University, Stanford, CA 94305-2125
  • Email: bump@gauss.stanford.edu
  • Solomon Friedberg
  • Affiliation: Department of Mathematics, University of California Santa Cruz, Santa Cruz, CA 95064
  • MR Author ID: 192407
  • ORCID: 0000-0002-1246-7738
  • Email: friedbe@cats.ucsc.edu
  • Jeffrey Hoffstein
  • Affiliation: Department of Mathematics, Brown University, Providence, RI 02912
  • MR Author ID: 87085
  • Email: jhoff@gauss.math.brown.edu
  • Additional Notes: Research supported by NSA grant MDA904-95-H-1053 (Friedberg) and by NSF grants DMS-9346517 (Bump) and DMS-9322150 (Hoffstein).
  • © Copyright 1996 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 33 (1996), 157-175
  • MSC (1991): Primary 11F66; Secondary 11F70, 11M41, 11N75
  • DOI: https://doi.org/10.1090/S0273-0979-96-00654-4
  • MathSciNet review: 1359575