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arXiv · 2112.05441

Equidistribution of exponential sums indexed by a subgroup of fixed cardinality

Théo Untrau
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Abstract

We consider families of exponential sums indexed by a subgroup of invertible classes modulo some prime power $q$. For fixed $d$, we restrict to moduli $q$ so that there is a unique subgroup of invertible classes modulo $q$ of order $d$. We study distribution properties of these families of sums as $q$ grows and we establish equidistribution results in some regions of the complex plane which are described as the image of a multi-dimensional torus via an explicit Laurent polynomial. In some cases, the region of equidistribution can be interpreted as the one delimited by a hypocycloid, or as a Minkowski sum of such regions.

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Théo Untrau. 2021-12-10. Equidistribution of exponential sums indexed by a subgroup of fixed cardinality. https://arxiv.org/abs/2112.05441

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