Experiments with zeta zeros and Perron's formula

Details Experiments with zeta zeros and Perron's formula Experiments with zeta zeros and Perron's formula

2011-03-31

arxiv.org/abs/1103.6226v1

Mathematics

Number Theory

76 pages

Scientific paper

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 $\phi$ function and other arithmetical functions. This is largely a
presentation of experimental results.

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