Abstract view
Values of Twisted Tensor $L$functions of Automorphic Forms Over Imaginary Quadratic Fields


Published:20140318
Printed: Oct 2014
Dominic Lanphier,
Department of Mathematics, Western Kentucky University, Bowling Green, KY 42101
Howard Skogman,
Department of Mathematics, SUNY Brockport, Brockport, NY 14420
Abstract
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 $GL_2(\mathbb{A}_K)$,
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.