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Values of Twisted Tensor L-functions of Automorphic Forms Over Imaginary Quadratic Fields

Published online by Cambridge University Press:  20 November 2018

Dominic Lanphier ,
Howard Skogman  and
Hiroyuki Ochiai
Dominic Lanphier
Affiliation:
Department of Mathematics, Western Kentucky UniversityBowling Green, KY 42101. e-mail: dominic.lanphier@wku.edu
Howard Skogman
Affiliation:
Department of Mathematics, SUNY Brockport, BrockportNY 14420. e-mail: hskogman@brockport.edu
Hiroyuki Ochiai
Affiliation:
Institute of Mathematics for Industry, Kyushu University, Motooka, Fukuoka, 819-0395, Japan. e-mail: ochiai@imi.kyushu-u.ac.jp
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Abstract

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Let $K$ be a complex quadratic extension of $\mathbb{Q}$ and let ${{\mathbb{A}}_{K}}$ denote the adeles of $K$. We find special values at all of the critical points of twisted tensor $L$-functions attached to cohomological cuspforms on $G{{L}_{2}}\left( {{\mathbb{A}}_{K}} \right)$ and establish Galois equivariance of the values. To investigate the values, we determine the archimedean factors of a class of integral representations of these $L$-functions, thus proving a conjecture due to Ghate. We also investigate analytic properties of these $L$-functions, such as their functional equations.

Keywords

11F6711F37twisted tensor L-functioncuspform, hypergeometric series
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 66 , Issue 5 , 01 October 2014 , pp. 1078 - 1109
Copyright
Copyright © Canadian Mathematical Society 2014

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