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PreprintCC BY 4.0arXiv

Hecke modules associated to certain ternary lattices of half-discriminant p2 and 4p2

  • Giovanna De Lauri
  • Dan Fretwell
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Abstract

We consider Hecke modules of orthogonal modular forms attached to definite ternary lattices of half-discriminant p2 with p prime and 4p2 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.

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Cite

BibTeXRIS
BibTeX
@misc{lauri2026hecke,
  title = {{Hecke modules associated to certain ternary lattices of half-discriminant $p^2$ and $4p^2$}},
  author = {Giovanna De Lauri and Dan Fretwell},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13295},
  eprint = {2610.13295},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13295},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Hecke modules associated to certain ternary lattices of half-discriminant p^2 and 4p^2
AU  - Giovanna De Lauri
AU  - Dan Fretwell
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.13295
UR  - https://arxiv.org/abs/2610.13295
AB  - 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.
ER  -