Quaternionic Gamma functions and their logarithmic derivatives as spectral functions

Details Quaternionic Gamma functions and their logarithmic derivatives as spectral functions Quaternionic Gamma functions and their logarithmic derivatives as spectral functions

1999-04-12

arxiv.org/abs/math/9904044v2

Math. Res. Lett. 8 (2001), no. 1-2, 209-223

Mathematics

Number Theory

latex2e, 22 pages. Includes previously separate paper math/9907103

Scientific paper

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''.)

Affiliated with

Also associated with

No associations

Rating

Quaternionic Gamma functions and their logarithmic derivatives as spectral functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quaternionic Gamma functions and their logarithmic derivatives as spectral functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quaternionic Gamma functions and their logarithmic derivatives as spectral functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-346346