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This article gives upper bounds on the number of Fourier-Jacobi coefficients that determine a paramodular cusp form in degree two. The level~N of the paramodular group is completely general throughout. Additionally, spaces of Jacobi cusp forms are spanned by using the theory of theta blocks due to Gritsenko, Skoruppa and Zagier. We combine these two techniques to rigorously compute spaces of paramodular cusp forms and to verify the Paramodular Conjecture of Brumer and Kramer in many cases of low level. The proofs rely on a detailed description of the zero dimensional cusps for the subgroup of integral elements in each paramodular group.
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참고문헌 (36)
참고문헌 신청
H. Aoki / 2000 / Estimating Siegel modular forms of genus 2 using Jacobi forms / J. Math. Kyoto Univ 40(3):581~588
S. Böcherer / 2012 / Surjectivity of Siegel Φ-operator for square free level and small weight / Ann. Inst. Fourier 62(1):121~144
J. Breeding / Author’s website
A. Brumer / 2014 / Paramodular abelian varieties of odd conductor / Trans. Amer. Math. Soc 366(5):2463~2516
J. Brunier / Vector valued formal Fourier-Jacobi expansions / arXiv:1303.3699.2013
S. Böcherer / 2012 / Surjectivity of Siegel Φ-operator for square free level and small weight / Ann. Inst. Fourier 62(1):121~144
J. Breeding / Author’s website
A. Brumer / 2014 / Paramodular abelian varieties of odd conductor / Trans. Amer. Math. Soc 366(5):2463~2516
J. Brunier / Vector valued formal Fourier-Jacobi expansions / arXiv:1303.3699.2013
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