Koshliakov kernel and identities involving the Riemann zeta function

Atul Dixit , Nicolas Robles , Arindam Roy , Alexandru Zaharescu

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classification 🧮 math.NT math.CA

keywords identitiesinvolvingfunctionfunctionskernelriemannzetabessel

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Some integral identities involving the Riemann zeta function and functions reciprocal in a kernel involving the Bessel functions $J_{z}(x), Y_{z}(x)$ and $K_{z}(x)$ are studied. Interesting special cases of these identities are derived, one of which is connected to a well-known transformation due to Ramanujan, and Guinand.

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Koshliakov kernel and identities involving the Riemann zeta function

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