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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

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

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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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


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:
  • 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:
  • Jeffrey Hoffstein
  • Affiliation: Department of Mathematics, Brown University, Providence, RI 02912
  • MR Author ID: 87085
  • Email:
  • 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:
  • MathSciNet review: 1359575