Advanced Studies in Pure Mathematics

Integral operators arising from the Riemann zeta function

Masatoshi Suzuki

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Abstract

In this paper we have two issues coming from the same background. The first one is to describe a certain ratio of Fredholm determinants of integral operators arising from the Riemann zeta function by using the solution of a single integral equation. The second one is to introduce a new integral operator arising from the Riemann zeta function and to study its basic analytic properties.

Article information

Source
Various Aspects of Multiple Zeta Functions — in honor of Professor Kohji Matsumoto's 60th birthday, H. Mishou, T. Nakamura, M. Suzuki and Y. Umegaki, eds. (Tokyo: Mathematical Society of Japan, 2020), 399-411

Dates
Received: 11 April 2018
Revised: 22 August 2018
First available in Project Euclid: 27 May 2020

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1590597097

Digital Object Identifier
doi:10.2969/aspm/08410399

Subjects
Primary: 11M06: $\zeta (s)$ and $L(s, \chi)$ 45A05: Linear integral equations 33B15: Gamma, beta and polygamma functions

Citation

Suzuki, Masatoshi. Integral operators arising from the Riemann zeta function. Various Aspects of Multiple Zeta Functions — in honor of Professor Kohji Matsumoto's 60th birthday, 399--411, Mathematical Society of Japan, Tokyo, Japan, 2020. doi:10.2969/aspm/08410399. https://projecteuclid.org/euclid.aspm/1590597097


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