Abstract
We show that a weak form of the generalized Böcherer conjecture implies multiplicity one for Siegel cusp forms of degree 2.
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Notes
For definitions and background on Siegel cusp forms, see [7].
Recall that an integer n is a fundamental discriminant if either n is a squarefree integer congruent to 1 modulo 4 or n=4m where m is a squarefree integer congruent to 2 or 3 modulo 4.
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Saha, A. A relation between multiplicity one and Böcherer’s conjecture. Ramanujan J 33, 263–268 (2014). https://doi.org/10.1007/s11139-013-9489-8
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DOI: https://doi.org/10.1007/s11139-013-9489-8
Keywords
- Siegel modular forms
- Multiplicity one
- Special values
- L-functions
- Automorphic forms
- Bocherer’s conjecture
- Fourier coefficients