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PreprintCC BY 4.0arXiv

Hecke modules associated to certain even ternary lattices of half-discriminant N2

  • Samadrito Bhattacharyya
  • Giovanna De Lauri
  • Dan Fretwell
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Abstract

We consider Hecke modules of orthogonal modular forms attached to definite even ternary lattices of half-discriminant N2, where N > 1 is odd and square-free. We prove explicit Jacquet-Langlands style correspondences with spaces of classical modular forms (in the spirit of Birch and Hein-Tornaria-Voight). 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{bhattacharyya2026hecke,
  title = {{Hecke modules associated to certain even ternary lattices of half-discriminant $\mathbfN^2$}},
  author = {Samadrito Bhattacharyya and Giovanna De Lauri and Dan Fretwell},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.16505},
  eprint = {2610.16505},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.16505},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Hecke modules associated to certain even ternary lattices of half-discriminant N^2
AU  - Samadrito Bhattacharyya
AU  - Giovanna De Lauri
AU  - Dan Fretwell
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.16505
UR  - https://arxiv.org/abs/2610.16505
AB  - We consider Hecke modules of orthogonal modular forms attached to definite even ternary lattices of half-discriminant N^2, where N > 1 is odd and square-free. We prove explicit Jacquet-Langlands style correspondences with spaces of classical modular forms (in the spirit of Birch and Hein-Tornaria-Voight). This is done by applying sequences of Watson-style transformations that reduce the discriminant while preserving the adelic orthogonal group.
ER  -