On Riesz Means of the Coefficients of Epstein’s Zeta Functions View Full Text


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Article Info

DATE

2018-11

AUTHORS

O. M. Fomenko

ABSTRACT

Let rk(n) denote the number of lattice points on a k-dimensional sphere of radius n. The generating functionζks=∑n=1∞rknn−s,k≥2, is Epstein’s zeta function. The paper considers the Riesz mean of the typeDρxζ3=1Γρ+1∑n≤xx−nρr3n, where ρ > 0; the error term Δρ(x; ζ3) is defined byDρxζ3=π3/2xρ+3/2Γρ+5/2+xρΓρ+1ζ30+Δρxζ3. K. Chandrasekharan and R. Narasimhan (1962, MR25#3911) proved thatΔρxζ3={O(x1/2+ρ/2)ρ>1,Ω±x1/2+ρ/2ρ≥0. In the present paper, it is proved thatΔρxζ3={Oxlogxρ=1,Ox2/3+ρ/3+ε1/2<ρ<1,Ox3/4+ρ/4+ε0<ρ≤1/2, and the Riesz means of the coefficients of ζk(s), k ≥ 4, are studied. More... »

PAGES

737-749

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10958-018-4039-y

DOI

http://dx.doi.org/10.1007/s10958-018-4039-y

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1106906286


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