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Displaying similar documents to “On Siegel modular forms”

Heegner cycles, modular forms and jacobi forms

Nils-Peter Skoruppa (1991)

Journal de théorie des nombres de Bordeaux

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We give a geometric interpretation of an arithmetic rule to generate explicit formulas for the Fourier coefficients of elliptic modular forms and their associated Jacobi forms. We discuss applications of these formulas and derive as an example a criterion similar to Tunnel's criterion for a number to be a congruent number.

Congruences between Siegel modular forms on the level of group cohomology

Karsten Buecker (1996)

Annales de l'institut Fourier

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Vector-valued Siegel modular forms may be found in certain cohomology groups with coefficients lying in an irreducible representation of the symplectic group. Using functoriality in the coefficients, we show that the components of the cohomology are independent of the weight parameter. The meaning of depends on a choice of parabolic subgroup of G S p ( 4 ) , giving a particular direction in the change of weight. Our results complement those of Taylor and Tilouine-Urban for the two other possible...

Surjectivity of Siegel Φ -operator for square free level and small weight

Siegfried Böcherer, Tomoyoshi Ibukiyama (2012)

Annales de l’institut Fourier

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We show the surjectivity of the (global) Siegel Φ -operator for modular forms for certain congruence subgroups of Sp ( 2 , ℤ ) and weight k = 4 , where the standard techniques (Poincaré series or Klingen-Eisenstein series) are no longer available. Our main tools are theta series and genus versions of basis problems.

Exceptional modular form of weight 4 on an exceptional domain contained in C.

Henry H. Kim (1993)

Revista Matemática Iberoamericana

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Resnikoff [12] proved that weights of a non trivial singular modular form should be integral multiples of 1/2, 1, 2, 4 for the Siegel, Hermitian, quaternion and exceptional cases, respectively. The θ-functions in the Siegel, Hermitian and quaternion cases provide examples of singular modular forms (Krieg [10]). Shimura [15] obtained a modular form of half-integral weight by analytically continuing an Eisenstein series. Bump and Bailey suggested the possibility of applying an analogue...