Quaternionic Gamma functions and their logarithmic derivatives as spectral functions
数论
2016-09-07 v2
摘要
We establish Connes's local trace formula (related to the explicit formulae of number theory) for the quaternions. This is done as an application of a study of the central operator H = log(|x|) + log(|y|) in the context of invariant harmonic analysis. The multiplicative analysis of the additive Fourier transform gives a spectral interpretation to generalized ``Tate Gamma functions'' (closely akin to the Godement-Jacquet ``\gamma(s,\pi,\psi)'' functions.) The analysis of H leads furthermore to a spectral interpretation for the logarithmic derivatives of these Gamma functions (which are involved in ``explicit formulae''.)
引用
@article{arxiv.math/9904044,
title = {Quaternionic Gamma functions and their logarithmic derivatives as spectral functions},
author = {Jean-Francois Burnol},
journal= {arXiv preprint arXiv:math/9904044},
year = {2016}
}
备注
latex2e, 22 pages. Includes previously separate paper math/9907103