Some sums over the non-trivial zeros of the Riemann zeta function

Jesús Guillera

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arXiv · 1307.5723

Some sums over the non-trivial zeros of the Riemann zeta function

Jesús Guillera

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Abstract

We prove some identities, which involve the non-trivial zeros of the Riemann zeta function. From them we derive some convergent asymptotic expansions related to the work by Cramér, and also new representations for some arithmetical functions in terms of the non-trivial zeros.

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Jesús Guillera. 2014-06-19. Some sums over the non-trivial zeros of the Riemann zeta function. https://arxiv.org/abs/1307.5723

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