Modular forms on noncongruence subgroups and Atkin-Swinnerton-Dyer relations
Liqun Fang, J. William Hoffman, Benjamin Linowitz, Andrew Rupinski,, Helena Verrill
TL;DR
This paper presents new examples of weight three cusp forms on noncongruence subgroups with modular Scholl representations that satisfy Atkin-Swinnerton-Dyer relations, expanding understanding of their arithmetic properties.
Contribution
It introduces novel examples of noncongruence cusp forms with modular Scholl representations and verifies Atkin-Swinnerton-Dyer relations for these cases.
Findings
New examples of noncongruence cusp forms with modular Scholl representations
Verification of three-term Atkin-Swinnerton-Dyer relations for these forms
Enhanced understanding of the arithmetic properties of noncongruence forms
Abstract
We give new examples of weight three cusp forms on noncongruence subgroups of SL(2, Z) whose Scholl representation is modular and which satisfy three term Atkin-Swinnerton-Dyer relations.
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 · Finite Group Theory Research · Algebraic Geometry and Number Theory