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- Title
Equidistribution of exponential sums indexed by a subgroup of fixed cardinality.
- Authors
UNTRAU, THÉO
- 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.
- Subjects
EXPONENTIAL sums; TORUS; POLYNOMIALS
- Publication
Mathematical Proceedings of the Cambridge Philosophical Society, 2024, Vol 176, Issue 1, p65
- ISSN
0305-0041
- Publication type
Article
- DOI
10.1017/S0305004123000361