Murmurations of modular forms in the weight aspect
Abstract
We prove the existence of "murmurations" in the family of holomorphic modular forms of level $1$ and weight $k\to\infty$, that is, correlations between their root numbers and Hecke eigenvalues at primes growing in proportion to the analytic conductor. This is the first demonstration of murmurations in an archimedean family.
Fields of Study & Subjects
Advanced Algebra and Geometry
Analytic Number Theory Research
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Algebra & Number Theory
- Volume
- 20
- Issue
- 2
- Pages
- 299–332
- Publication date
- 16 February 2026
- Language
- EN