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Integral operators arising from the Riemann zeta function. (English) Zbl 1451.11091
Mishou, Hidehiko (ed.) et al., Various aspects of multiple zeta functions – in honor of Professor Kohji Matsumoto’s 60th birthday. Proceedings of the international conference, Nagoya University, Nagoya, Japan August 21–25, 2020. Tokyo: Mathematical Society of Japan. Adv. Stud. Pure Math. 84, 399-411 (2020).
Summary: 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.
For the entire collection see [Zbl 1446.11004].
MSC:
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
45A05 Linear integral equations
33B15 Gamma, beta and polygamma functions
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[10] Department of Mathematics, School of Science, Tokyo Institute of Technology
[11] 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, JAPAN
[12] E-mail address:msuzuki@math.
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