Jiri Janacek, Institute of Physiology, Academy of Sciences of the Czech Republic, Videnska 1083, 142 20 Praha, Czech Republic e-mail: janacek@biomed.cas.cz
Abstract: Values of the Epstein zeta function of a positive definite matrix and the knowledge of matrices with minimal values of the Epstein zeta function are important in various mathematical disciplines. Analytic expressions for the matrix theta functions of integral matrices can be used for evaluation of the Epstein zeta function of matrices. As an example, principal coefficients in asymptotic expansions of variance of the lattice point count in the random ball are calculated for some lattices.
Keywords: Epstein zeta function, Riemann theta function, variance of volume estimate, Rankin-Sobolev problem
Classification (MSC 2000): 33F05, 60D05
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