On calculation of zeta function of integral matrix
Mathematica Bohemica (2009)
- Volume: 134, Issue: 1, page 49-58
- ISSN: 0862-7959
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topJanáček, Jiří. "On calculation of zeta function of integral matrix." Mathematica Bohemica 134.1 (2009): 49-58. <http://eudml.org/doc/38072>.
@article{Janáček2009,
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.},
author = {Janáček, Jiří},
journal = {Mathematica Bohemica},
keywords = {Epstein zeta function; Riemann theta function; variance of volume estimate; Rankin-Sobolev problem; Epstein zeta function; Riemann theta function; variance of volume estimate; Rankin-Sobolev problem},
language = {eng},
number = {1},
pages = {49-58},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On calculation of zeta function of integral matrix},
url = {http://eudml.org/doc/38072},
volume = {134},
year = {2009},
}
TY - JOUR
AU - Janáček, Jiří
TI - On calculation of zeta function of integral matrix
JO - Mathematica Bohemica
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 134
IS - 1
SP - 49
EP - 58
AB - 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.
LA - eng
KW - Epstein zeta function; Riemann theta function; variance of volume estimate; Rankin-Sobolev problem; Epstein zeta function; Riemann theta function; variance of volume estimate; Rankin-Sobolev problem
UR - http://eudml.org/doc/38072
ER -
References
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- Janáček, J., Variance of periodic measure of bounded set with random position, Comment. Math. Univ. Carolinae 47 (2006), 473-482. (2006) Zbl1150.62315MR2281006
- Kendall, D. G., Rankin, R. A., 10.1093/qmath/4.1.178, Quarterly J. Math., 2nd Ser. 4 (1953), 178-189. (1953) Zbl0052.14503MR0057484DOI10.1093/qmath/4.1.178
- Rankin, R. A., 10.1017/S2040618500035668, Proc. Glasgow. Math. Assoc. 1 (1953), 149-158. (1953) Zbl0052.28005MR0059300DOI10.1017/S2040618500035668
- Sobolev, S. L., Formulas for mechanical cubatures in -dimensional space, Dokl. Akad. Nauk SSSR 137 (1961), 527-530. (1961) Zbl0196.49202MR0129548
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