相关论文: Poincar\'e and Eisenstein series for Jacobi forms …

In this text we generalize the classical Jacobi Eisenstein series as they were discussed by Eichler and Zagier to arbitrary lattices. We use two different methods to derive the general Fourier expansion. The last two sections give formulas…

We prove that under suitable conditions, the Jacobi Poincar\'{e} series of exponential type of integer weight and matrix index does not vanish identically. For classical Jacobi forms, we construct a basis consisting of the "first" few…

We show that all Eichler integrals, and more generally all "generalized second order modular forms" can be expressed as linear combinations of corresponding generalized second order Eisenstein series with coefficients in classical modular…

We compute the Fourier expansion of vector valued Eisenstein series for the Weil representation associated to an even lattice. To this end, we define certain twists by Dirichlet characters of the usual Eisenstein series associated to…

We derive new Poincar\'e-series representations for infinite families of non-holomorphic modular invariant functions that include modular graph forms as they appear in the low-energy expansion of closed-string scattering amplitudes at genus…

This paper has three main objectives: (i) To establish an isomorphism between Jacobi forms of index $D_{2n+1}$ (lattice index) and elliptic modular forms of level $2$. (ii) To provide an explicit formula for the Fourier coefficients of…

We give a short and "soft" proof of the asymptotic orthogonality of Fourier coefficients of Poincar\'e series for classical modular forms as well as for Siegel cusp forms, in a qualitative form.

We calculate the Jacobi Eisenstein series of weight $k \ge 3$ for a certain representation of the Jacobi group, and evaluate these at $z = 0$ to give coefficient formulas for a family of modular forms $Q_{k,m,\beta}$ of weight $k \ge 5/2$…

We define Jacobi forms of indefinite lattice index, and show that they are isomorphic to vector-valued modular forms also in this setting. We also consider several operations of the two types of objects, and obtain an interesting bilinear…

We consider Fuchsian singularities of arbitrary genus and prove, in a conceptual manner, a formula for their Poincar\'e series. This uses Coxeter elements involving Eichler-Siegel transformations. We give geometrical interpretations for the…

We will characterize the Eisenstein series for O(2, n + 2) as a particular Hecke eigenform. As an application we show that it belongs to the associated Maa{\ss} space. If the underlying lattice is even and unimodular, this leads to an…

We compute the Fourier coefficients of analogues of Kohnen and Zagier's modular forms $f_{k,D}$ of weight $2$ and negative discriminant. These functions can also be written as twisted traces of certain weight $2$ Poincar\'e series with…

We compute explicit formulae for the constant terms and Fourier coefficients for Eisenstein series on $\operatorname{Sp}(4,\mathbb{R})$, in terms of zeta functions and Whittaker functions. We also develop a generalisation of Ramanujan sums…

In this work we give an explicit formula for the Fourier coefficients of Eisenstein series corresponding to certain arithmetic lattices acting on hyperbolic n+1-space. As a consequence we obtain results on location of all poles of these…

The purpose of this paper is to solve various differential equations having Eisenstein series as coefficients using various tools and techniques. The solutions are given in terms of modular forms, modular functions and equivariant forms.

In this paper we consider Jacobi forms of half-integral index for any positive definite lattice L (classical Jacobi forms from the book of Eichler and Zagier correspond to the lattice A_1=<2>). We give a lot of examples of Jacobi forms of…

We give a list of $113$ holomorphic eta-quotients of integral weight ($66$ of which are primitive) and provide a uniform closed formula for their Fourier coefficients $c(l)$ where $l\equiv1\bmod{m}$ with some fixed $m\mid24$. The proof…

Using deformed or twisted Eisenstein Series, we construct a Jacobi-Serre derivative on even-weight Jacobi forms that generalizes the classical Serre derivative on modular forms. As an application, we obtain Ramanujan equations for the index…

We derive the Fourier expansion of scalar-valued Eisenstein series for O(2, n+2) using classical methods of Siegel, Braun, Zagier, Bruinier and others. We assume that the underlying lattice splits two hyperbolic planes. Finally we prove for…

Let $N$ be a normal subgroup of a finite group $G$ and $V$ be a fixed finite-dimensional $G$-module. The Poincar\'{e} series for the multiplicities of induced modules and restriction modules in the tensor algebra $T(V)=\oplus_{k \geq…