### Estimates for Fourier coefficients of Siegel cusp forms of degree two

Winfried Kohnen (1993)

Compositio Mathematica

Similarity:

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

Winfried Kohnen (1993)

Compositio Mathematica

Similarity:

Heim, Bernhard (2010)

International Journal of Mathematics and Mathematical Sciences

Similarity:

Nils-Peter Skoruppa (1991)

Journal de théorie des nombres de Bordeaux

Similarity:

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.

Karsten Buecker (1996)

Annales de l'institut Fourier

Similarity:

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 $GSp\left(4\right)$, giving a particular direction in the change of weight. Our results complement those of Taylor and Tilouine-Urban for the two other possible...

Siegfried Böcherer, Tomoyoshi Ibukiyama (2012)

Annales de l’institut Fourier

Similarity:

We show the surjectivity of the (global) Siegel $\Phi $-operator for modular forms for certain congruence subgroups of $\mathrm{Sp}(2,\mathbb{Z})$ 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.

Shinji Fukuhara (2012)

Acta Arithmetica

Similarity:

Rainer Schulze-Pillot (1995)

Journal de théorie des nombres de Bordeaux

Similarity:

Henry H. Kim (1993)

Revista Matemática Iberoamericana

Similarity:

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...

Tomoyoshi Ibukiyama (1985)

Journal für die reine und angewandte Mathematik

Similarity: