Work

Hecke modules associated to certain ternary lattices of half-discriminant $p^2$ and $4p^2$

Year: 2026

Type: preprint

Abstract: We consider Hecke modules of orthogonal modular forms attached to definite ternary lattices of half-discriminant $p^2$ with $p$ prime and $4p^2$ with $p$ an odd prime. Where possible, we prove explicit Jacquet-Langlands style correspondences with spaces of classical modular forms (in the spirit of Birch and Hein-Tornaria-Voight), and give conjectures for the remaining genera. This is done by applying sequences of Watson-style transformations that reduce the discriminant while preserving the adelic orthogonal group.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.13295

Authors: De Lauri, Giovanna, Fretwell, Dan

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7221511874

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