منابع مشابه
The Action of the Heat Operator on Jacobi Forms
We investigate the action of the heat operator on Jacobi forms. In particular, we present two explicit characterizations of this action on Jacobi forms of index 1. Furthermore, we study congruences and filtrations of Jacobi forms. As an application, we determine when an analog of Atkin’s U-operator applied to a Jacobi form is nonzero modulo a prime.
متن کاملHarmonic Morphisms and the Jacobi Operator
We prove that harmonic morphisms preserve the Jacobi operator along harmonic maps. We apply this result to prove infinitesimal and local rigidity (in the sense of Toth) of harmonic morphisms to a sphere. 1. Harmonic morphisms Harmonic maps φ : (M, g) → (N, h) between two smooth Riemannian manifolds are critical points of the energy functional E(φ,Ω) = 1 2 ∫ Ω |dφ| dvg for any compact domain Ω ⊆...
متن کاملOzeki Polynomials and Jacobi Forms
A Jacobi polynomial was introduced by Ozeki. It corresponds to the codes over F2. Later, Bannai and Ozeki showed how to construct Jacobi forms with various index using a Jacobi polynomial corresponding to the binary codes. It generalizes Broué-Enguehard map. In this paper, we study Jacobi polynomial which corresponds to the codes over F2f . We show how to construct Jacobi forms with various ind...
متن کاملTernary codes and Jacobi forms
In this paper we study the bivariate theta-series which can be attached to the complete weight enumerator of ternary codes. We give an injective homorphism between the ring of invariants of a certain matrix group and the ring of Jacobi modular forms. This generalizes to Jacobi forms a result of Brou% e and Enguehard [Ann. Sci. % Ecole Norm. Sup. 5 (4) (1972) 157–181] on classical modular forms....
متن کاملThe Mordell Integral, Quantum Modular Forms, and Mock Jacobi Forms
It is explained how the Mordell integral ∫ R e −2πzx cosh(πx) dx unifies the mock theta functions, partial (or false) theta functions, and some of Zagier’s quantum modular forms. As an application, we exploit the connections between q-hypergeometric series and mock and partial theta functions to obtain finite evaluations of the Mordell integral for rational choices of τ and z. 1. The Mordell In...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1998
ISSN: 0019-2082
DOI: 10.1215/ijm/1256045039