Bounded exponential sums with multiplicative coefficients
Abstract
Abstract We investigate when the exponential sum is bounded, for a multiplicative function and . We show that under natural assumptions, is bounded only when is very close to a twisted Dirichlet character . We obtain sharper classification results for functions that are completely multiplicative or take only finitely many values, including a complete classification in the case when is completely multiplicative and is irrational. We also prove a stronger classification under the assumption that the sum is bounded for a positive measure set of .
Fields of Study & Subjects
advanced mathematical theories
Analytic Number Theory Research
Advanced Algebra and Geometry
Publication details
- Journal / source
- Mathematika
- Volume
- 72
- Issue
- 4
- Publication date
- 24 July 2026
- Language
- EN