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arXiv · 2311.07657

The Riemann zeta function and exact exponential sum identities of divisor functions

Maria Nastasescu·Nicolas Robles·Bogdan Stoica·Alexandru Zaharescu
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Abstract

We prove an explicit integral formula for computing the product of two shifted Riemann zeta functions everywhere in the complex plane. We show that this formula implies the existence of infinite families of exact exponential sum identities involving the divisor functions, and we provide examples of these identities. We conjecturally propose a method to compute divisor functions by matrix inversion, without employing arithmetic techniques.

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Maria Nastasescu, Nicolas Robles, Bogdan Stoica, Alexandru Zaharescu. 2023-11-13. The Riemann zeta function and exact exponential sum identities of divisor functions. https://arxiv.org/abs/2311.07657

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