论文信息 - Jacobi forms over totally real number fields

Jacobi forms over totally real number fields

We define Jacobi forms over a totally real algebraic number field K and construct examples by first embedding the group and the space into the symplectic group and the symplectic upper half space respectively. Then symplectic modular forms are created and Jacobi forms arise by taking the appropriate Fourier coefficients. Also some known relations of Jacobi forms to vector valued modular forms over rational numbers are extended to totally real fields.

Howard Skogman

[1] A. Krieg. The Maaß spaces on the Hermitian half-space of degree 2 , 1991 .

[2] Jacobi functions and Euler products for Hermitian modular forms , 1992 .

[3] C. Ziegler,et al. Jacobi forms of higher degree , 1989 .

[4] L. Vaserstein. ON THE GROUP SL2 OVER DEDEKIND RINGS OF ARITHMETIC TYPE , 1972 .

[5] George E. Cooke,et al. A weakening of the euclidean property for integral domains and applications to algebraic number theory. II. , 1976 .

[6] Klaus K. Haverkamp. Hermitian Jacobi Forms , 1996 .

[7] S. Friedberg. On theta functions associated to indefinite quadratic forms , 1986 .

[8] C. Jacobi,et al. Fundamenta nova theoriae functionum ellipticarum , 1829 .

[9] Bernhard Liehl,et al. On the group S L 2 over orders of arithmetic type. , 1981 .