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arXiv · 2408.04247

Shifted second moment of the Riemann zeta function and a Fourier type kernel

Parikshit Dutta·Debashis Ghoshal·Krishnan Rajkumar
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Abstract

We compute the second moment of the Riemann zeta function for shifted arguments over a domain that extends the ones in the literature. We use the Riemann-Siegel formula for the error term in the approximate functional equation and take the products of all the terms into account. We also show that, as a function of imaginary shifts on the critical line, the the second moment behaves like a Fourier-Cauchy type kernel on a class of functions. This is reminiscent of orthogonal functions.

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Parikshit Dutta, Debashis Ghoshal, Krishnan Rajkumar. 2024-08-08. Shifted second moment of the Riemann zeta function and a Fourier type kernel. https://arxiv.org/abs/2408.04247

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