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Start Over Creator Janáček, Jiří

1. Asymptotics of variance of the lattice point count

Creator:
Janáček, Jiří
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
point lattice, Fourier transform, volume, and variance
Language:
English
Description:
The variance of the number of lattice points inside the dilated bounded set $rD$ with random position in $\Bbb R^d$ has asymptotics $\sim r^{d-1}$ if the rotational average of the squared modulus of the Fourier transform of the set is $O(\rho ^{-d-1})$. The asymptotics follow from Wiener's Tauberian theorem.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. On calculation of zeta function of integral matrix

Creator:
Janáček, Jiří
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Epstein zeta function, Riemann theta function, variance of volume estimate, and Rankin-Sobolev problem
Language:
English
Description:
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.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public