Related papers: Eisenstein series identities based on partial frac…

We study the (mock) Eisenstein series $E_k$ of weight $k \in \{1,3/2,2\}$ for the Weil representation on an even lattice, defined as the result of Bruinier and Kuss's coefficient formula for the Eisenstein series naively evaluated at $k$.…

We investigate the relation between Klingen's decomposition of the space of Siegel modular forms and Dulinski's analogous decomposition of the space of Jacobi forms.

Recently, Amderberhan, Griffin, Ono, and Singh started the study of "traces of partition Eisenstein series" and used it to give explicit formulas for many interesting functions. In this note we determine the precise spaces in which they…

We locate the zeros of the modular forms $E_k^2(\tau) + E_{2k}(\tau), E_k^3(\tau) + E_{3k} (\tau),$ and $E_k(\tau)E_l(\tau) +E_{k+l}(\tau),$ where $E_k(\tau)$ is the Eisenstein series for the full modular group $\text{SL}_2(\mathbb{Z})$. By…

Let $k,N \in \mathbb{N}$ with $N$ square-free and $k>1$. We prove an orthogonal relation and use this to compute the Fourier coefficients of the Eisenstein part of any $f(z) \in M_{2k}(\Gamma_0(N))$ in terms of sum of divisors function. In…

We examine the zeros of newform Eisenstein series $E_{\chi_1,\chi_2,k}(z)$ of weight $k$ on $\Gamma_0(q_1 q_2)$, where $\chi_1$ and $\chi_2$ are primitive characters modulo $q_1$ and $q_2$, respectively. We determine the location and…

We obtain pullback formulas for Klingen Eisenstein series with arbitrary levels, with respect to both Siegel congruence and paramodular subgroups, in degree two. Pullback results are used, along with the Fourier series expansion of Klingen…

We show that an elliptic modular form with integral Fourier coefficients in a number field $K$, for which all but finitely many coefficients are divisible by a prime ideal $\frak{p}$ of $K$, is a constant modulo $\frak{p}$. A similar…

We give a formula for certain values and derivatives of Siegel series and use them to compute Fourier coefficients of derivatives of the Siegel Eisenstein series of weight g/2 and genus g. When g=4, the Fourier coefficient is approximated…

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 use the description of the Picard modular surface for discriminant $-3$ as a moduli space of curves of genus $3$ to generate all vector-valued Picard modular forms from bi-covariants for the action of ${GL}_2$ on the space of pairs of…

In this article we define the algebra of differential modular forms and we prove that it is generated by Eisenstein series of weight $2,4$ and 6. We define Hecke operators on them, find some analytic relations between these Eisenstein…

If $p\geq 5$ is prime and $k\geq 4$ is an even integer with $(p-1)\nmid k$ we consider the Eisenstein series $G_k$ on $\operatorname{SL}_2(\mathbb{Z})$ modulo powers of $p$. It is classically known that for such $k$ we have $G_k\equiv…

We study equivariant primitives of Eisenstein series for principal congruence subgroups and show that they are precisely the corresponding non-holomorphic Eisenstein series. We present closed formulas that naturally generalise existing…

We study "partition Eisenstein series", extensions of the Eisenstein series $G_{2k}(\tau),$ defined by $$\lambda=(1^{m_1}, 2^{m_2},\dots, k^{m_k}) \vdash k \ \ \ \ \ \longmapsto \ \ \ \ \ G_{\lambda}(\tau):= G_2(\tau)^{m_1}…

A set of nonlinear differential equations associated with the Eisenstein series of the congruent subgroup $\Gamma_0(2)$ of the modular group $SL_2(\mathbb{Z})$ is constructed. These nonlinear equations are analogues of the well known…

Notable results on the special values of $L$-functions of Siegel modular forms were obtained by J. Sturm in the case when the degree $n$ is even and the weight $k$ is an integer. In this paper we extend this method to half-integer weights…

In this paper we investigate a result of Ueno on the modularity of generating series associated to the zeta functions of binary Hermitian forms previously studied by Elstrodt et al. We improve his result by showing that the generating…

We study expansions of Drinfeld modular forms of rank \(r \geq 2\) along the boundary of moduli varieties. Product formulas for the discriminant forms \(\Delta_{\mathfrak{n}}\) are developed, which are analogous with Jacobi's formula for…

We introduce a new family of real analytic modular forms on the upper half plane. They are arguably the simplest class of `mixed' versions of modular forms of level one and are constructed out of real and imaginary parts of iterated…