The weighted Selberg integral is a discrete mean-square, that is a generalization of the classical Selberg integral of primes toan arithmetic function $f$, whose values in a short interval are suitably attached to a weight function. We give conditions on $f$ and select a particular class of weights, in order to investigate non-trivial bounds of weighted Selberg integrals of both $f$ and $fastmu$. In particular, we discuss the cases of the symmetry integral and the modified Selberg integral, the latter involving the Cesaro weight. We also prove some side results when $f$ is a divisor function.

Symmetry and short interval mean-squares

COPPOLA, GIOVANNI;LAPORTA, MAURIZIO
2017

Abstract

The weighted Selberg integral is a discrete mean-square, that is a generalization of the classical Selberg integral of primes toan arithmetic function $f$, whose values in a short interval are suitably attached to a weight function. We give conditions on $f$ and select a particular class of weights, in order to investigate non-trivial bounds of weighted Selberg integrals of both $f$ and $fastmu$. In particular, we discuss the cases of the symmetry integral and the modified Selberg integral, the latter involving the Cesaro weight. We also prove some side results when $f$ is a divisor function.
5-7846-0144-X
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11588/585460
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