Abstract
Let $K$ be a function field of odd characteristic, and let $\pi$ (resp., $\eta$) be a cuspidal automorphic representation of ${\rm GL}\sb 2(\mathbb {A}\sb K)$ (resp., ${\rm GL}\sb 1(\mathbb {A}\sb K)$). Then we show that a weighted sum of the twists of $L(s,\pi)$ by quadratic characters $\chi\sb D,\sum \sb DL(s,\pi\otimes \sp \chi\sb D)a\sb 0(s,\pi,D)\eta(D)|D|\sp {-w}$, is a rational function and has a finite, nonabelian group of functional equations. A similar construction in the noncuspidal cases gives a rational function of three variables. We specify the possible denominators and the degrees of the numerators of these rational functions. By rewriting this object as a multiple Dirichlet series, we also give a new description of the weight functions $a\sb 0(s,\pi,D)$ originally considered by D. Bump, S. Friedberg and J. Hoffstein.
Citation
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
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