Related papers: Vector Valued Siegel Modular Forms for \Gamma_2[2,…

In this semi-expository note, we give a new proof of a structure theorem due to Shimura for nearly holomorphic modular forms on the complex upper half plane. Roughly speaking, the theorem says that the space of all nearly holomorphic…

For positive integers $g$ and $N$, let $\mathcal{F}_N$ be the field of meromorphic Siegel modular functions of genus $g$ and level $N$ whose Fourier coefficients belong to the $N$th cyclotomic field. We present explicit generators of…

Let $\rho$ denote an irreducible two-dimensional representation of $\Gamma_{0}(2)$. The collection of vector-valued modular forms for $\rho$, which we denote by $M(\rho)$, form a graded and free module of rank two over the ring of modular…

We extend Igusa's map $\rho$ to modular forms which vanish on the hyperelliptic locus of the Siegel upper half-plane. The lowest non-vanishing derivatives of such modular forms are computed with the help of the general Thomae formula, they…

In this paper, we investigate linear relations among regularized motivic iterated integrals on $\mathbb{P}^{1}\setminus\{0,1,\infty\}$ of depth two, which we call regularized motivic double zeta values. Some mysterious connections between…

The level moduli space $A_g^{4,8}$ is mapped to the projective space by means of gradients of odd Theta functions, such a map turning out no to be injective in the genus 2 case. In this work a congruence subgroup $\Gamma$ is located between…

We discuss two simple but useful observations that allow the construction of modular forms from given ones using invariant theory. The first one deals with elliptic modular forms and their derivatives, and generalizes the Rankin-Cohen…

In this paper, we introduce higher level versions of the theta group $\Gamma_{\theta}.$ In particular, we treat level 3 and 4 versions of the theta group, $\Gamma_{\theta,3}$ and $\Gamma_{\theta,4}$ and prove that $\displaystyle…

We present bases for certain spaces of meromorphic vector-valued rational-weight mock modular forms constructed using Rademacher sums.

We will give the graded ring of Siegel modular forms of degree two with respect to a non-split symplectic group explicitly.

We extend the framework of modular invariant supersymmetric theories to encompass invariance under more general discrete groups $\Gamma$, that allow the presence of several moduli and make connection with the theory of automorphic forms.…

False theta functions form a family of functions with intriguing modular properties and connections to mock modular forms. In this paper, we take the first step towards investigating modular transformations of higher rank false theta…

Unlike classical modular forms, there is currently no general way to implement the computation of Siegel modular forms of arbitrary weight, level and character, even in degree two. There is however, a way to do it in a unified way. After…

Let $g$ be a principal modulus with rational Fourier coefficients for a discrete subgroup of $\mathrm{SL}_2(\mathbb{R})$ between $\Gamma(N)$ or $\Gamma_0(N)^\dag$ for a positive integer $N$. Let $K$ be an imaginary quadratic field. We give…

We develop a theory of weights for a quantum analogue of the symmetric pair (gl4,gl2 x gl2) realised as a quantum symmetric pair subalgebra. Based on Letzter's triangular decomposition we define Verma modules. Using magical operators that…

We study the $\mthbb{Q}$-vector space generated by the double zeta values with character of conductor $4$. For this purpose, we define associated double Eisenstein series and investigate their relation with modular forms of level $4$.

We revisit the modular flavor symmetry from a more general perspective. The scalar modular forms of principal congruence subgroups are extended to the vector-valued modular forms, then we have more possible finite modular groups including…

We prove that all mod $p^m$ singular forms of level $N$, degree $n+r$, and $p$-rank $r$ with $n\ge r$ are congruent mod $p^m$ to linear combinations of theta series of degree $r$ attached to quadratic forms of some level. Moreover, we prove…

In this work we use the Rankin-Selberg method to obtain results on the analytic properties of the standard $L$-function attached to vector valued Siegel modular forms. In particular we provide a detailed description of its possible poles…

Moduli spaces of stable coherent sheaves on a surface are of much interest for both mathematics and physics. Yoshioka computed generating functions of Poincare polynomials of such moduli spaces if the surface is the projective plane P2 and…