Pointwise and correlation bounds on Dedekind sums over small subgroups
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910334365728768 |
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| author | Borda, Bence Munsch, Marc Shparlinski, Igor |
| author_facet | Borda, Bence Munsch, Marc Shparlinski, Igor |
| contents | We obtain new bounds, pointwisely and on average, for Dedekind sums $\mathsf{s}(λ,p)$ modulo a prime $p$ with $λ$ of small multiplicative order $d$ modulo $p$. Assuming the infinitude of Mersenne primes, the range of our results is optimal. Moreover, we relate high moments of $L(1,χ)$ over subgroups of characters to some correlations of Dedekind sums and use our recent results to study these correlations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_04304 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Pointwise and correlation bounds on Dedekind sums over small subgroups Borda, Bence Munsch, Marc Shparlinski, Igor Number Theory 11F20, 11J71, 11K38, 11M20 We obtain new bounds, pointwisely and on average, for Dedekind sums $\mathsf{s}(λ,p)$ modulo a prime $p$ with $λ$ of small multiplicative order $d$ modulo $p$. Assuming the infinitude of Mersenne primes, the range of our results is optimal. Moreover, we relate high moments of $L(1,χ)$ over subgroups of characters to some correlations of Dedekind sums and use our recent results to study these correlations. |
| title | Pointwise and correlation bounds on Dedekind sums over small subgroups |
| topic | Number Theory 11F20, 11J71, 11K38, 11M20 |
| url | https://arxiv.org/abs/2305.04304 |