相关论文: On the space of theta functions for a prime level

In this article we give an analogue of Hecke and Sturm bounds for Hilbert modular forms over real quadratic fields. Let $K$ be a real quadratic field and $\Om_K$ its ring of integers. Let $\Gamma$ be a congruence subgroup of $\SL_2(\Om_K)$…

We consider quantum symmetric algebras, FRT bialgebras and, more generally, intertwining algebras for pairs of Hecke symmetries which represent quantum hom-spaces. The paper makes an attempt to investigate Koszulness and Gorensteinness of…

A basis for the space of generalized theta functions of level one for the spin groups, parameterized by the theta characteristics (the even theta characteristcs for the odd spin groups) on a curve, is shown to be projectively flat over the…

This paper is a survey on the role of Higgs bundle theory in the study of higher Teichm\"uller spaces. Recall that the Teichm\"uller space of a compact surface can be identified with a certain connected component of the moduli space of…

We define theta blocks as products of Jacobi theta functions divided by powers of the Dedekind eta-function and show that they give a powerful new method to construct Jacobi forms and Siegel modular forms, with applications also in lattice…

In this article, we determine the trace of some Hecke operators on the spaces of level one automorphic forms on the special orthogonal groups of the euclidean lattices $\mathrm{E}_7$, $\mathrm{E}_8$ and $\mathrm{E}_8\oplus \mathrm{A}_1$,…

We study the action of the derived Hecke algebra in the setting of dihedral weight one forms, and prove a conjecture of the second- and fourth- named authors relating this action to certain Stark units associated to the symmetric square…

The purpose of this article is to give a simple and explicit construction of mock modular forms whose shadows are Eisenstein series of arbitrary integral weight, level, and character. As application, we construct forms whose shadows are…

We study the moduli space of Gieseker semi-stable sheaves on the complex projective plane supported on sextic curves and having Euler characteristic one. We determine locally free resolutions of length one for all such sheaves. We decompose…

We show that some $q$-series such as universal mock theta functions are linear sums of theta quotients and mock Jacobi forms of weight 1/2, which become holomorphic parts of real analytic modular forms when they are restricted to torsion…

We continue our study of Yoshida's lifting, which associates to a pair of automorphic forms on the adelic multiplicative group of a quaternion algebra a Siegel modular form of degree 2. We consider here the case that the automorphic forms…

In this paper, we study the diagonal restrictions of certain Hilbert theta series for a totally real field $F$, and prove that they span the corresponding space of elliptic modular forms when the $F$ is quadratic or cubic. Furthermore, we…

The prime number decomposition of a finite dimensional Hilbert space reflects itself in the representations that the space accommodates. The representations appear in conjugate pairs for factorization to two relative prime factors which can…

In the 80's Kudla and Millson introduced a theta function in two variables. It behaves as a Siegel modular form with respect to the first variable, and is a closed differential form on an orthogonal Shimura variety with respect to the other…

Generalizing a result of~\cite{Z1991} for modular forms of level~one, we give a closed formula for the sum of all Hecke eigenforms on $\Gamma_0(N)$, multiplied by their odd period polynomials in two variables, as a single product of Jacobi…

We study p-divisibility of discriminants of Hecke algebras associated to spaces of cusp forms of prime level. We make a precise conjecture about the indexes of Hecke algebras in their normalisation which implies (if true) the conjecture…

In this short paper, we find the transformation formula for the theta series under the action of the Jacobi modular group on the Siegel-Jacobi space. This formula generalizes the formula (5.1) obtained by Mumford in his book[p.189, Tata…

The nilpotence order of the mod 2 Hecke operators. Let $\Delta=\sum_{m=0}^\infty q^{(2m+1)^2} \in F_2[[q]]$ be the reduction mod 2 of the $\Delta$ series. A modular form f modulo 2 of level 1 is a polynomial in $\Delta$. If p is an odd…

A well-known observation of Serre and Tate is that the Hecke algebra acts locally nilpotently on modular forms mod 2 on $\mathrm{SL}_2(\mathbb{Z})$. We give an algorithm for calculating the degree of Hecke nilpotency for cusp forms, and we…

Recently, Allen, Grove, Long, and Tu proposed an explicit Hypergeometric-Modularity method which gives a concrete link between certain hypergeometric objects and modular forms. The theory is exemplified by a collection of 199 weight 3…