Jacobi forms of indefinite lattice index

Generalized Inequalities for Indefinite Forms

We establish abstract inequalities that give, as particular cases, many previously established Hölder-like inequalities. In addition to unifying the proofs of these inequalities, which, in most cases, tend to be technical and obscure, the proofs of our inequalities are quite simple and basic. Moreover, we show that sharper inequalities can be obtained by applying our results.

On Congruences of Jacobi Forms

We consider congruences and filtrations of Jacobi forms. More specifically, we extend Tate’s theory of theta cycles to Jacobi forms, which allows us to prove a criterion for an analog of Atkin’s U-operator applied to a Jacobi form to be nonzero modulo a prime.

Jacobi Forms of Degree One

We show that a certain subspace of space of elliptic cusp forms is isomorphic as a Hecke module to a certain subspace of space of Jacobi cusp forms of degree one with matrix index by constructing an explicit lifting. This is a partial generalization of the work of Skoruppa and Zagier. This lifting is also related with the Ikeda lifting.

Neighbors of Indefinite Binary Quadratic Forms

In this paper, we derive some algebraic identities on right and left neighbors R(F ) and L(F ) of an indefinite binary quadratic form F = F (x, y) = ax + bxy + cy of discriminant Δ = b − 4ac. We prove that the proper cycle of F can be given by using its consecutive left neighbors. Also we construct a connection between right and left neighbors of F . Keywords—Quadratic form, indefinite form, cy...

On successive minima of indefinite quadratic forms