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15 April 2003 Sums of twisted GL(2) L-functions over function fields
Benji Fisher, Solomon Friedberg
Duke Math. J. 117(3): 543-570 (15 April 2003). DOI: 10.1215/S0012-7094-03-11735-4

Abstract

Let $K$ be a function field of odd characteristic, and let $\pi$(resp., $\eta$) be a cuspidal automorphic representation of ${\rmGL}\sb 2(\mathbb {A}\sb K)$ (resp., ${\rm GL}\sb 1(\mathbb {A}\sbK)$). Then we show that a weighted sum of the twists of $L(s,\pi)$ byquadratic characters $\chi\sb D,\sum \sb DL(s,\pi\otimes \sp \chi\sbD)a\sb 0(s,\pi,D)\eta(D)|D|\sp {-w}$, is a rational function and has afinite, nonabelian group of functional equations. A similarconstruction in the noncuspidal cases gives a rational function ofthree variables. We specify the possible denominators and the degreesof the numerators of these rational functions. By rewriting thisobject as a multiple Dirichlet series, we also give a new descriptionof the weight functions $a\sb 0(s,\pi,D)$ originally considered byD. Bump, S. Friedberg and J. Hoffstein.

Citation

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Benji Fisher. Solomon Friedberg. "Sums of twisted GL(2) L-functions over function fields." Duke Math. J. 117 (3) 543 - 570, 15 April 2003. https://doi.org/10.1215/S0012-7094-03-11735-4

Information

Published: 15 April 2003
First available in Project Euclid: 26 May 2004

zbMATH: 1048.11039
MathSciNet: MR1979053
Digital Object Identifier: 10.1215/S0012-7094-03-11735-4

Subjects:
Primary: 11F70
Secondary: 11M38

Rights: Copyright © 2003 Duke University Press

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Vol.117 • No. 3 • 15 April 2003
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