Geodesic
On calculation of zeta function of integral matrix
Mathematica Bohemica, Tome 134 (2009) no. 1, pp. 49-58
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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.
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.
DOI : 10.21136/MB.2009.140639
Classification : 33F05, 60D05
Keywords: Epstein zeta function; Riemann theta function; variance of volume estimate; Rankin-Sobolev problem 
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Janáček, Jiří. On calculation of zeta function of integral matrix. Mathematica Bohemica, Tome 134 (2009) no. 1, pp. 49-58. doi: 10.21136/MB.2009.140639

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