Triple sums of Kloosterman sums and the discrepancy of modular inverses

Valentin Blomer; Morten S. Risager; Igor E. Shparlinski

doi:10.48550/arXiv.2411.17823

Triple sums of Kloosterman sums and the discrepancy of modular inverses

Valentin Blomer, Morten S. Risager, Igor E. Shparlinski

Department of Mathematical Sciences

Research output: Working paper › Preprint › Research

Abstract

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.

Original language	English
Publisher	arxiv.org
Number of pages	27
DOIs	https://doi.org/10.48550/arXiv.2411.17823
Publication status	Published - 2024

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Cite this

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abstract = "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.",

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AB - 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.

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