An omega result for the least negative Hecke eigenvalue
Abstract
Abstract We establish the existence of many holomorphic Hecke eigenforms of large weight for the full modular group, for which the least positive integer such that satisfies . This is believed to be best possible up to the term in the exponent, and improves on a result of Kowalski, Lau, Soundararajan and Wu, who showed that, when restricted to primes, the least prime such that can be as large as . We also discuss an extension of our result to primitive holomorphic cusp forms of weight and squarefree level .
Fields of Study & Subjects
Analytic Number Theory Research
Advanced Algebra and Geometry
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 9
- Publication date
- 1 September 2026
- Language
- EN