Symmetry and short interval mean-squares
| Autor: | Coppola, Giovanni, Laporta, Maurizio |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Proc. Steklov Inst. Math. 299.1 (2017), 56-77 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1134/S0081543817080041 |
| Popis: | The weighted Selberg integral is a discrete mean-square, that is a generalization of 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 $f\ast\mu$. 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. Comment: Through an optimal Lemma 3 we correct our Theorem 1 proof |
| Databáze: | arXiv |
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