Symmetry and Short Interval Mean-Squares

Article

Abstract

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 * μ. 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.

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© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.University of SalernoFisciano (SA)Italy
  2. 2.Dipartimento di Matematica e Applicazioni “R. Caccioppoli,”Università degli Studi di Napoli Federico II, Complesso di Monte S. AngeloNapoliItaly

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