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EnglishThe 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.
| Titolo: | Symmetry and short interval mean-squares | |
| Autori: | LAPORTA, MAURIZIO (Corresponding) | |
| Data di pubblicazione: | 2017 | |
| Rivista: | ||
| 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. | |
| Handle: | http://hdl.handle.net/11588/585460 | |
| ISBN: | 5-7846-0144-X | |
| Appare nelle tipologie: | 4.1 Articoli in Atti di convegno |
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