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arXiv · 2604.26234

The $p$-powers dividing certain exponential sums

Antonine Phigareau
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Abstract

We define the notion of couple density $(D, \mathbf b)$ where $D$ is a non-empty subset of $\mathbb Z^{m}$ and $ \mathbf b$ a fixed element in $\{0, \cdots, q-2\}^{m};$ We determine a minimum in terms of the density of the couple $(D,\mathbf b)$ for the $q$-adic valuation of the sum $ S_{\ell}(F,\mathbf b)$ with $F$ a Laurent polynomial. And we show that this minimum is a bound for the $q$-adic valuation of the zeros and poles of the associated $L$-function.

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Antonine Phigareau. 2026-04-29. The $p$-powers dividing certain exponential sums. https://arxiv.org/abs/2604.26234

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