Symmetry and short interval mean-squares

Giovanni Coppola ; Maurizio Laporta

Informatics and Automation, Analytic number theory, Tome 299 (2017), pp. 62-85.

Résumé

The weighted Selberg integral is a discrete mean-square that generalizes the classical Selberg integral of primes to an 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 $f*\mu $. 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.

Détail

Keywords: mean square, short interval, symmetry, correlation.

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