On calculation of zeta function of integral matrix. (English) Zbl 1212.33012

Summary: 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 the 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.


33F05 Numerical approximation and evaluation of special functions
60D05 Geometric probability and stochastic geometry