Theta and zeta functions for odd-dimensional locally symmetric spaces of rank one

TL;DR

This paper extends the study of theta and zeta functions to odd-dimensional real hyperbolic manifolds, highlighting the role of eta invariants and their connection to super theta and zeta functions.

Contribution

It introduces the analysis of theta and zeta functions for odd-dimensional rank one symmetric spaces, focusing on the appearance of eta invariants.

Findings

Identification of eta invariants in odd-dimensional cases

Extension of previous even-dimensional results

Insights into super theta and zeta functions

Abstract

This paper is a continuation of our work on theta and zeta functions In the previous papers we considered the case of even dimensional rank one symmetric spaces of non-compact type. The present is concerned with the odd-dimensional case, i.e. with odd-dimensional real hyperbolic manifolds. It is the natural appearence of eta invariants in connection with super theta and zeta functions what makes this case particularly interesting. (authors name corrected)