Sign patterns of Fourier coefficients of modular forms
Andrew R. Booker
TL;DR
This paper establishes conditions where the sign patterns of Fourier coefficients uniquely determine a self-dual holomorphic cusp form up to scalar multiples.
Contribution
It introduces criteria linking Fourier coefficient signs to the unique identification of certain modular forms, advancing understanding of their structure.
Findings
Sign patterns can determine the form up to scalar multiple
Conditions for uniqueness based on Fourier signs
Enhanced understanding of modular form structure
Abstract
We give conditions under which a self-dual holomorphic cusp form is determined up to scalar multiplication by the signs of its Fourier coefficients.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Analytic Number Theory Research