Related papers: Automatic convergence for Siegel modular forms

We prove that weights of two Siegel modular forms of nonquadratic nebentypus should satisfy some congruence relations if these modular forms are congruent to each other. Applying this result, we prove that there are no mod $p$ singular…

In this paper, we discuss the theory of the Siegel modular variety in the aspects of arithmetic and geometry. This article covers the theory of Siegel modular forms, the Hecke theory, a lifting of elliptic cusp forms, geometric properties…

Siegel's action is generalized to the D=2(p+1) (p even) dimensional space-time. The investigation of self-duality of chiral p-forms is extended to the momentum frame, using Siegel's action of chiral bosons in two space-time dimensions and…

We extend some results of Gun, Murty, and Rath on elliptic modular forms. We take ANY Fuchsian triangle group with a cusp and look at power series expansions in a natural parameter around that cusp. Consider the automorphic forms for such a…

We prove the following statement about any Siegel modular form $F$ of degree $n$ and arbitrary odd level $N$ on the group $\Gamma_{0}^{(n)}(N)$. Let $A(F,T)$ denote the Fourier coefficients of $F$ and write $T=(T(i,j))$. Suppose that $F$…

We prove that formal Fourier Jacobi expansions of degree 2 are Siegel modular forms. As a corollary, we deduce modularity of the generating function of special cycles of codimension 2, which were defined by Kudla. A second application is…

We study the coherent cohomology of automorphic sheaves corresponding to Siegel modular forms $f$ of low weight on ${\rm GSp}(4)$ Shimura varieties. Inspired by the work of Prasanna--Venkatesh on singular cohomology of locally symmetric…

This work considers aspects of almost holomorphic and meromorphic Siegel modular forms from the perspective of physics and mathematics. The first part is concerned with (refined) topological string theory and the direct integration of the…

In this paper, we prove a conjecture of Broadhurst and Zudilin \cite{BZ17} concerning a divisibility property of the Fourier coefficients of a meromorphic modular form using the generalization of the Shimura lift by Borcherds…

In this paper, we decompose the space of nearly holomorphic Hilbert-Siegel automorphic forms as representations of the adele group under certain assumptions. We also give an application for classical holomorphic Hilbert-Siegel modular…

We prove an arithmetic Hilbert-Samuel type theorem for semi-positive singular hermitian line bundles of finite height. In particular, the theorem applies to the log-singular metrics of Burgos-Kramer-K\"uhn. Our theorem is thus suitable for…

The theory of quaternionic modular forms has been studied for decades as an example of the modular forms of many variables. The purpose of this study is to provide some congruence relations satisfied by such quaternionic modular forms.

We investigate under what conditions holomorphic forms defined on the regular locus of a reduced complex space extend to holomorphic (or logarithmic) forms on a resolution of singularities. We give a simple necessary and sufficient…

Starting from the results in math.DG:1212.3161 we prove that for a given Bianchi group, certain natural coefficent modules and a lot of sequences of congruence subgroups of the size of the torsion subgroup of the first homology grows…

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.…

We prove an equidistribution theorem for a family of holomorphic Siegel cusp forms for $GSp_4/\mathbb{Q}$ in various aspects. A main tool is Arthur's invariant trace formula. While Shin and Shin-Templier used Euler-Poincar\'e functions at…

The Springer modules have a combinatorial property called ``coincidence of dimensions,'' i.e., the Springer modules are naturally decomposed into submodules with common dimensions. Morita and Nakajima proved the property by giving modules…

We investigate Poincar\'e series, where we average products of terms of Fourier series of real-analytic Siegel modular forms. There are some (trivial) special cases for which the products of terms of Fourier series of elliptic modular forms…

We prove in this paper the original version of Kontsevich and Soibelman's motivic integral identity conjecture for formal functions by developing a novel framework for equivariant motivic integration on special rigid varieties. This theory…

We prove the convergence of normal form power series for suitably nonsingular analytic submanifolds under a broad class of infinite-dimensional Lie pseudo-group actions. Our theorem is illustrated by a number of examples, and includes, as a…