Jacobi forms with CM and applications
نویسندگان
چکیده
We define Jacobi forms with complex multiplication. Analogous to modular multiplication, they are constructed from Hecke characters of the associated imaginary quadratic field. From this construction we obtain a form which specializes η(τ)26 present highlight an open question Dyson and Serre. give other examples applications multiplication including constructing theta blocks elliptic curves new families congruences cranks for certain partition functions.
منابع مشابه
Extended Jacobi and Laguerre Functions and their Applications
The aim of this paper is to introduce two new extensions of the Jacobi and Laguerre polynomials as the eigenfunctions of two non-classical Sturm-Liouville problems. We prove some important properties of these operators such as: These sets of functions are orthogonal with respect to a positive de nite inner product de ned over the compact intervals [-1, 1] and [0,1), respectively and also th...
متن کاملAn Explicit Construction of Jacobi Cusp Forms and Its Applications
From an elliptic cusp form, we construct a Jacobi cusp form of degree one with matrix index, which gives a section of the descent map. We have applications to the theory of Maass spaces on orthogonal groups and the Ikeda lifting.
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 کاملJacobi Forms over Number Fields
OF THE DISSERTATION Jacobi Forms over Number Fields by Howard Skogman Doctor of Philosophy in Mathematics University of California San Diego, 1999 Professor Harold Stark, Chair We de ne Jacobi Forms over an algebraic number eld K and construct examples by rst embedding the group and the space into the symplectic group and the symplectic upper half space respectively. We then create symplectic m...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2023
ISSN: ['0022-314X', '1096-1658']
DOI: https://doi.org/10.1016/j.jnt.2022.11.014