Symmetry and Short Interval Mean-Squares
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.
Unable to display preview. Download preview PDF.
- 2.G. Coppola, “On the symmetry of arithmetical functions in almost all short intervals. V,” arXiv: 0901.4738 [math.NT].Google Scholar
- 3.G. Coppola, “On the modified Selberg integral,” arXiv: 1006.1229 [math.NT].Google Scholar
- 17.G. Kolesnik, “On the estimation of multiple exponential sums,” in Recent Progress in Analytic Number Theory: Durham Symp. 1979 (Academic, London, 1981), Vol. 1, pp. 231–246.Google Scholar