Koecher-Maass series of the Ikeda lift for U(m,m)
Number Theory
2015-11-03 v2
Abstract
Let K be an imaginary quadratic field with discriminant -D, and x the Dirichlet character corresponding to the extension K/Q. Let m=2n or 2n+1 with n a positive integer. Let f be a primitive form of weight 2k+1 and level D with Neben character x, or a primitive form of weight 2k for SL(2,Z) according as m=2n, or m=2n+1. For such an f let I(m,f) be the lift of f to the space of Hermitian modular forms of degree m constructed by Ikeda. We then give an explicit formula of the Koecher-Maass series L(s,I(m,f)) of I(m,f). This is a generalization of [Y. Mizuno, Manuscripta Math. 119(2006), 175-216].
Keywords
Cite
@article{arxiv.1403.2175,
title = {Koecher-Maass series of the Ikeda lift for U(m,m)},
author = {Hidenori Katsurada},
journal= {arXiv preprint arXiv:1403.2175},
year = {2015}
}
Comments
This paper will appear in Kyoto Journal of Mathematics. arXiv admin note: substantial text overlap with arXiv:1102.4393