Memorandum on Dimension Formulas for Spaces of Jacobi Forms
نویسنده
چکیده
We state ready to compute dimension formulas for the spaces of Jacobi cusp forms of integral weight k and integral scalar index m on subgroups of SL(2,Z).
منابع مشابه
Dimension Formulas for Automorphic Forms of Coabelian Hyperbolic Type
There are infinitely many hyperbolic transforms of complex abelian surfaces. The corresponding universal covers change from the complex plane to the unit ball, from flat to hyperbolic metrics. Looking back to Jacobi’s periodic functions we were able to construct 2-dimensional abelian functions transformable to automorphic forms on the ball. In this article we prove explicit dimension formulas f...
متن کاملN ov 2 00 7 Jacobi Forms of Degree One and Weil Representations Nils
We discuss the notion of Jacobi forms of degree one with matrix index, we state dimension formulas, give explicit examples, and indicate how closely their theory is connected to the theory of invariants of Weil representations associated to finite quadratic modules. 1 Jacobi forms of degree one Jacobi forms of degree one with matrix index F gained recent interest, mainly due to applications in ...
متن کاملExact Formulas for Coefficients of Jacobi Forms
In previous work, we introduced harmonic Maass-Jacobi forms. The space of such forms includes the classical Jacobi forms and certain Maass-Jacobi-Poincaré series, as well as Zwegers’ real-analytic Jacobi forms, which play an important role in the study of mock theta functions and related objects. Harmonic Maass-Jacobi forms decompose naturally into holomorphic and non-holomorphic parts. In this...
متن کاملSzegö quadrature formulas for certain Jacobi-type weight functions
In this paper we are concerned with the estimation of integrals on the unit circle of the form ∫ 2π 0 f(eiθ)ω(θ)dθ by means of the so-called Szegö quadrature formulas, i.e., formulas of the type ∑n j=1 λjf(xj) with distinct nodes on the unit circle, exactly integrating Laurent polynomials in subspaces of dimension as high as possible. When considering certain weight functions ω(θ) related to th...
متن کاملA pr 1 99 6 HIGHER WEIL - PETERSSON VOLUMES OF MODULI SPACES OF STABLE n - POINTED CURVES
Moduli spaces of compact stable n-pointed curves carry a hierarchy of cohomology classes of top dimension which generalize the Weil-Petersson volume forms and constitute a version of Mumford classes. We give various new formulas for the integrals of these forms and their generating functions.
متن کامل