Experiments with zeta zeros and Perron's formula

Robert Baillie

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arXiv · 1103.6226

Experiments with zeta zeros and Perron's formula

Robert Baillie

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Abstract

Of what use are the zeros of the Riemann zeta function? We can use sums involving zeta zeros to count the primes up to $x$. Perron's formula leads to sums over zeta zeros that can count the squarefree integers up to $x$, or tally Euler's $ϕ$ function and other arithmetical functions. This is largely a presentation of experimental results.

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BibTeX RIS

Robert Baillie. 2011-03-31. Experiments with zeta zeros and Perron's formula. https://arxiv.org/abs/1103.6226

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