On the mean value of a kind of zeta functions

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2014Embargo end date: 01 Dec 2012 English Publisher:Institute of Mathematics, Polish Academy of SciencesJournal:Acta Arithmetica, volume 166, pages 33-54 (issn: 0065-1036, eissn: 1730-6264,

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Authors: Liu, Kui;

doi: 10.4064/aa166-1-4 , 10.48550/arxiv.1212.6513

arXiv: 1212.6513

On the mean value of a kind of zeta functions

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Abstract

Let $d_{α, β}(n)=\sum\limits_{\substack{n=kl αl1.$ It has an analytic continuation to $\Re s>1/3.$ We get an asymptotic formula for the mean square of $ζ_{α,β}(s)$ in the strip $1/2

Related Organizations

Qingdao University
China (People's Republic of)
Qingdao Binhai University
China (People's Republic of)

Keywords

Pythagorean triangles, Mathematics - Number Theory, Lattice points in specified regions, FOS: Mathematics, Number Theory (math.NT), Other Dirichlet series and zeta functions, Voronoi formula, zeta function

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