Modular Forms with Only Nonnegative Coefficients
Abstract
Abstract We study modular forms for $${\text{ SL }}_2(\mathbb {Z})$$ SL 2 ( Z ) with no negative Fourier coefficients. Let A ( k ) be the positive integer where if the first A ( k ) Fourier coefficients of a modular form of weight k for $${\text{ SL }}_2(\mathbb {Z})$$ SL 2 ( Z ) are nonnegative, then all of its Fourier coefficients are nonnegative, so that A ( k ) can be interpreted as a “nonnegativity Sturm bound”. We give upper and lower bounds for A ( k ), as well as an upper bound on the n th Fourier coefficient of any form with no negative Fourier coefficients.
Fields of Study & Subjects
Composite Structure Analysis and Optimization
Advanced Mathematical Modeling in Engineering
Structural Analysis and Optimization
Publication details
- Journal / source
- Research in Number Theory
- Publisher
- Springer Science and Business Media LLC
- Volume
- 12
- Issue
- 3
- Publication date
- 30 May 2026
- Language
- EN