Open Access
May 2017 On the product of Hurwitz zeta-functions
Nian Liang Wang, Soumyarup Banerjee
Proc. Japan Acad. Ser. A Math. Sci. 93(5): 31-36 (May 2017). DOI: 10.3792/pjaa.93.31


Corresponding to the lattice point problem for a random sphere Kendall and Rankin [8], Nakajima [9] considered the summatory function of the coefficients of the product of two Hurwitz zeta-functions and obtained the Bessel series expression. In this note we treat the case of the product of $\varkappa$ Hurwitz zeta-functions for an arbitrary integer $\varkappa\ge 2$ and obtain the expression in terms of the Voronoï-Steen function. This amounts to a refinement of corrected Nakajima’s formula with streamlining of the ambiguous argument.


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Nian Liang Wang. Soumyarup Banerjee. "On the product of Hurwitz zeta-functions." Proc. Japan Acad. Ser. A Math. Sci. 93 (5) 31 - 36, May 2017.


Published: May 2017
First available in Project Euclid: 29 April 2017

zbMATH: 06790306
MathSciNet: MR3645657
Digital Object Identifier: 10.3792/pjaa.93.31

Primary: 11A07
Secondary: 11M32

Keywords: Dirichlet divisor problem , Hurwitz zeta-function , Reisz sums

Rights: Copyright © 2017 The Japan Academy

Vol.93 • No. 5 • May 2017
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