Sturm type theorem for Siegel modular forms of degree 2

Details Sturm type theorem for Siegel modular forms of degree 2 Sturm type theorem for Siegel modular forms of degree 2

2011-01-15

arxiv.org/abs/1101.2986v2

Mathematics

Number Theory

This paper has been withdrawn by the author. About the results in this paper, the author have studied with Professor Y. Choie

Scientific paper

We attempt to generalize a congruence property of elliptic modular forms proved by Sturm to that of Haupttypus of Siegel modular forms of degree 2 with level. Namely, we give an explicit bound of Fourier coefficients required to determine the congruence of modular forms. We give the analog of Sturm's theorem for Jacobi forms, which is required in the proof. In the case that Nebentypus of Siegel modular forms with prime level, in order to prove the congruence between two modular forms, we show that it suffices to check the congruence of the finitely many Fourier coefficients. Finally, we give two examples of our main theorem.

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