A certain Dirichlet series attached to Siegel modular forms of degree two.
A decomposition theorem for Jacobi forms.
A generalization of the reciprocity law of multiple Dedekind sums
Various multiple Dedekind sums were introduced by B.C.Berndt, L.Carlitz, S.Egami, D.Zagier and A.Bayad.In this paper, noticing the Jacobi form in Bayad [4], the cotangent function in Zagier [23], Egami’s result on cotangent functions [14] and their reciprocity laws, we study a special case of the Jacobi forms in Bayad [4] and deduce a generalization of Egami’s result on cotangent functions and a generalization of Zagier’s result. Further, we consider their reciprocity laws.
A geometrical approach to the theory of Jacobi forms
A trace formula for Jacobi forms.
An arithmetic theory of Jacobi forms in higher dimensions.
Asymptotic formulae for partition ranks
Using an extension of Wright's version of the circle method, we obtain asymptotic formulae for partition ranks similar to formulae for partition cranks which where conjectured by F. Dyson and recently proved by the first author and K. Bringmann.
Asymptotic formulas for the coefficients of certain automorphic functions
We derive asymptotic formulas for the coefficients of certain classes of weakly holomorphic Jacobi forms and weakly holomorphic modular forms (not necessarily of integral weight) without using the circle method. Then two applications of these formulas are given. Namely, we estimate the growth of the Fourier coefficients of two important weak Jacobi forms of index 1 and non-positive weights and obtain an asymptotic formula for the Fourier coefficients of the modular functions for all integers k,l...
Automorphic forms on Os + 2,2(R) and infinte products.