On the mean value of a kind of zeta functions

• Autorzy: Kui Liu
• Języki publikacji: EN

Abstrakty

EN

Let $d_{α,β}(n) = ∑ _{n=kl, αl<k≤βl} 1$ be the number of ways of factoring n into two almost equal integers. For fixed rational numbers α > 0 and β > 0, we consider a zeta function of the type $ζ_{α,β}(s) = ∑_{n=1}^{∞} d_{α,β}(n)/n^{s}$ for ℜs > 1. It has an analytic continuation to ℜs > 1/3. We get an asymptotic formula for the mean square of $ζ_{α,β}(s)$ in the strip 1/2 < ℜs < 1. As an application, we improve a result on the distribution of primitive Pythagorean triangles.

Kategorie tematyczne

• 11M41: Other Dirichlet series and zeta functions
• 11P21: Lattice points in specified regions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 166
• Numer: 1
• Strony: 33-54

Daty

wydano

2014

Twórcy

autor

Kui Liu

• Department of Mathematics, Qingdao University, 266071, Qingdao, Shandong, China

Identyfikatory

DOI

10.4064/aa166-1-4