The Maclaurin spectral functions associated with the development of the heat kernel on
compact rank one symmetric spaces are analysed. Relations with various invariants most …

This book continues the applications of mathematics, more specifically of theta, eta, and zeta
functions, and modular forms, to various areas of theoretical physics. It is a follow-up and …

We define two types of Witten's zeta functions according to Cartan's classification of compact
symmetric spaces. The type II is the original Witten zeta function constructed by means of …

We assign to a non-compact Riemannian symmetric space X a theta function and a zeta
function. We compute all of the Minakshisundaram–Pleijel coefficients in a short-time …

We considered the Mellin transform assigned to the convolution wave kernel associated to
the Laplace-Beltrami operator on higher rank Riemannian symmetric spaces of the non …

This paper presents new spectral properties of the Laplacian on N-dimensional (N ≥ 1 N≥
1) noncompact rank one symmetric spaces X X. Two new classes of spectral functions …

The Mellin transform of the heat kernel on a non-compact symmetric space X gives rise to a
zeta function ζ (s; x, b) that was studied when the rank of X was 1. In this case the special …

The applications of theta, eta, and zeta functions, and of modular forms and elliptic functions
have increasingly become a part of the landscape of various facets of mathematical physics …

The Maclaurin spectral functions associated with the development of the heat kernel on
compact rank one symmetric spaces are analysed. Relations with various invariants most …

In this thesis we study topics pertaining to the analysis, geometry, and spectral theory of the
Laplacian on Riemannian symmetric spaces of rank one. These spaces are quotients of the …