Energy bounds for modular roots and their applications
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
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| _version_ | 1866909790626643968 |
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| author | Kerr, Bryce Shkredov, Ilya D. Shparlinski, Igor E. Zaharescu, Alexandru |
| author_facet | Kerr, Bryce Shkredov, Ilya D. Shparlinski, Igor E. Zaharescu, Alexandru |
| contents | We generalise and improve some recent bounds for additive energies of modular roots. Our arguments use a variety of techniques, including those from additive combinatorics, algebraic number theory and the geometry of numbers. We give applications of these results to new bounds on correlations between {\it Sali{é}} sums and to a new equidistribution estimate for the set of modular roots of primes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_09405 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Energy bounds for modular roots and their applications Kerr, Bryce Shkredov, Ilya D. Shparlinski, Igor E. Zaharescu, Alexandru Number Theory We generalise and improve some recent bounds for additive energies of modular roots. Our arguments use a variety of techniques, including those from additive combinatorics, algebraic number theory and the geometry of numbers. We give applications of these results to new bounds on correlations between {\it Sali{é}} sums and to a new equidistribution estimate for the set of modular roots of primes. |
| title | Energy bounds for modular roots and their applications |
| topic | Number Theory |
| url | https://arxiv.org/abs/2103.09405 |