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An explicit refined Gan--Gross--Prasad identity for Fourier--Jacobi periods of degree 2 Siegel cusp forms

  • Biplab Paul
  • Ameya Pitale
  • Abhishek Saha
  • Ralf Schmidt
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Abstract

We compute the local integrals appearing in the refined Gan--Gross--Prasad conjecture for Fourier--Jacobi periods of Sp4 in new ramified cases and use this to formulate an explicit conjectural identity relating Petersson norms of degree 2 Siegel cusp forms and associated half-integral weight forms. We note consequences of our identity for the growth of Petersson norms, the size of Fourier coefficients, and non-vanishing of central L-values.

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Cite

BibTeXRIS
BibTeX
@misc{paul2026explicit,
  title = {{An explicit refined Gan--Gross--Prasad identity for Fourier--Jacobi periods of degree 2 Siegel cusp forms}},
  author = {Biplab Paul and Ameya Pitale and Abhishek Saha and Ralf Schmidt},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.26007},
  eprint = {2608.26007},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.26007},
}
RIS
TY  - UNPB
TI  - An explicit refined Gan--Gross--Prasad identity for Fourier--Jacobi periods of degree 2 Siegel cusp forms
AU  - Biplab Paul
AU  - Ameya Pitale
AU  - Abhishek Saha
AU  - Ralf Schmidt
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2608.26007
UR  - https://arxiv.org/abs/2608.26007
AB  - We compute the local integrals appearing in the refined Gan--Gross--Prasad conjecture for Fourier--Jacobi periods of Sp_4 in new ramified cases and use this to formulate an explicit conjectural identity relating Petersson norms of degree 2 Siegel cusp forms and associated half-integral weight forms. We note consequences of our identity for the growth of Petersson norms, the size of Fourier coefficients, and non-vanishing of central L-values.
ER  -