Triple sums of Kloosterman sums and the discrepancy of modular inverses
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908497222828032 |
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| author | Blomer, Valentin Risager, Morten S. Shparlinski, Igor E. |
| author_facet | Blomer, Valentin Risager, Morten S. Shparlinski, Igor E. |
| contents | We investigate the distribution of modular inverses modulo positive integers $c$ in a large interval. We provide upper and lower bounds for their box, ball and isotropic discrepancy, thereby exhibiting some deviations from random point sets. The analysis is based, among other things, on a new bound for a triple sum of Kloosterman sums. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17823 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Triple sums of Kloosterman sums and the discrepancy of modular inverses Blomer, Valentin Risager, Morten S. Shparlinski, Igor E. Number Theory 11K38, 11L05, 11F12 We investigate the distribution of modular inverses modulo positive integers $c$ in a large interval. We provide upper and lower bounds for their box, ball and isotropic discrepancy, thereby exhibiting some deviations from random point sets. The analysis is based, among other things, on a new bound for a triple sum of Kloosterman sums. |
| title | Triple sums of Kloosterman sums and the discrepancy of modular inverses |
| topic | Number Theory 11K38, 11L05, 11F12 |
| url | https://arxiv.org/abs/2411.17823 |