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arXiv · 2309.05233

Uniform bounds for Kloosterman sums of half-integral weight, same-sign case

Qihang Sun
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Abstract

In the previous paper [Sun23], the author proved a uniform bound for sums of half-integral weight Kloosterman sums. This bound was applied to prove an exact formula for partitions of rank modulo 3. That uniform estimate provides a more precise bound for a certain class of multipliers compared to the 1983 result by Goldfeld and Sarnak and generalizes the 2009 result from Sarnak and Tsimerman to the half-integral weight case. However, the author only considered the case when the parameters satisfied $\tilde m\tilde n<0$. In this paper, we prove the same uniform bound when $\tilde m\tilde n>0$ for further applications.

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Qihang Sun. 2023-09-11. Uniform bounds for Kloosterman sums of half-integral weight, same-sign case. https://doi.org/10.1016/j.jnt.2024.11.012

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