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Title: On calculation of zeta function of integral matrix (English)
Author: Janáček, Jiří
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 134
Issue: 1
Year: 2009
Pages: 49-58
Summary lang: English
Category: math
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 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. (English)
Keyword: Epstein zeta function
Keyword: Riemann theta function
Keyword: variance of volume estimate
Keyword: Rankin-Sobolev problem
MSC: 33F05
MSC: 60D05
idZBL: Zbl 1212.33012
idMR: MR2504687
DOI: 10.21136/MB.2009.140639
Date available: 2010-07-20T17:46:59Z
Last updated: 2020-07-29
Stable URL:
Reference: [1] Conway, H., Sloane, N. J. A.: Sphere Packings, Lattices and Groups.Springer, New York (1998).
Reference: [2] Delone, B. N., Ryshkov, S. S.: A contribution to the theory of the extrema of a multi-dimensional $\zeta$-function.Dokl. Akad. Nauk SSSR 173 (1967), 991-994. MR 0220676
Reference: [3] Janáček, J.: Variance of periodic measure of bounded set with random position.Comment. Math. Univ. Carolinae 47 (2006), 473-482. Zbl 1150.62315, MR 2281006
Reference: [4] Kendall, D. G., Rankin, R. A.: On the number of points of a given lattice in a random hypersphere.Quarterly J. Math., 2nd Ser. 4 (1953), 178-189. Zbl 0052.14503, MR 0057484, 10.1093/qmath/4.1.178
Reference: [5] Rankin, R. A.: A minimum problem for the Epstein zeta function.Proc. Glasgow. Math. Assoc. 1 (1953), 149-158. Zbl 0052.28005, MR 0059300, 10.1017/S2040618500035668
Reference: [6] Sobolev, S. L.: Formulas for mechanical cubatures in $n$-dimensional space.Dokl. Akad. Nauk SSSR 137 (1961), 527-530. Zbl 0196.49202, MR 0129548


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