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arXiv · 2305.04304

Pointwise and correlation bounds on Dedekind sums over small subgroups

Bence Borda·Marc Munsch·Igor Shparlinski
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Abstract

We obtain new bounds, pointwisely and on average, for Dedekind sums $\mathsf{s}(\lambda,p)$ modulo a prime $p$ with $\lambda$ 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 $L(1,\chi)$ over subgroups of characters to some correlations of Dedekind sums and use our recent results to study these correlations.

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Bence Borda, Marc Munsch, Igor Shparlinski. 2023-05-07. Pointwise and correlation bounds on Dedekind sums over small subgroups. https://arxiv.org/abs/2305.04304

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