Article Dans Une Revue Mathematical Proceedings of the Cambridge Philosophical Society Année : 2023

Equidistribution of exponential sums indexed by a subgroup of fixed cardinality

Résumé

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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hal-05212971 , version 1 (18-08-2025)

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Théo Untrau. Equidistribution of exponential sums indexed by a subgroup of fixed cardinality. Mathematical Proceedings of the Cambridge Philosophical Society, 2023, 176 (1), pp.65-94. ⟨10.1017/S0305004123000361⟩. ⟨hal-05212971⟩
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