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On Some Applications of Automorphic Forms to Number Theory

Author(s): Daniel Bump; Solomon Friedberg; Jeffrey Hoffstein
Journal: Bull. Amer. Math. Soc. 33 (1996), 157-175.
MSC (1991): Primary 11F66; Secondary 11F70, 11M41, 11N75
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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
Email: friedbe@cats.ucsc.edu

Jeffrey Hoffstein
Affiliation: Department of Mathematics, Brown University, Providence, RI 02912
Email: jhoff@gauss.math.brown.edu

DOI: 10.1090/S0273-0979-96-00654-4
PII: S 0273-0979(96)00654-4
Additional Notes: Research supported by NSA grant MDA904-95-H-1053 (Friedberg) and by NSF grants DMS-9346517 (Bump) and DMS-9322150 (Hoffstein).
Copyright of article: Copyright 1996, American Mathematical Society

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