Proceedings of the Japan Academy, Series A, Mathematical Sciences

On the product of Hurwitz zeta-functions

Nian Liang Wang and Soumyarup Banerjee

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Abstract

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.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 93, Number 5 (2017), 31-36.

Dates
First available in Project Euclid: 29 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.pja/1493431380

Digital Object Identifier
doi:10.3792/pjaa.93.31

Mathematical Reviews number (MathSciNet)
MR3645657

Zentralblatt MATH identifier
06790306

Subjects
Primary: 11A07: Congruences; primitive roots; residue systems
Secondary: 11M32: Multiple Dirichlet series and zeta functions and multizeta values

Keywords
Hurwitz zeta-function Dirichlet divisor problem Reisz sums

Citation

Wang, Nian Liang; Banerjee, Soumyarup. On the product of Hurwitz zeta-functions. Proc. Japan Acad. Ser. A Math. Sci. 93 (2017), no. 5, 31--36. doi:10.3792/pjaa.93.31. https://projecteuclid.org/euclid.pja/1493431380


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