Related papers: Generators for modules of vector-valued Picard mod…

Inspired by Borcherds' questions, Guerzhoy constructed a new type of Hecke operators $\mathcal{T}(p)$, called the multiplicative Hecke operators, which acts on the space of meromorphic modular forms on the full modular group ${\rm SL}(\Z)$.…

An algorithm is given for computing explicit formulas for the generators of relations among the invariant rational functions for vector-valued bilinear forms. These formulas have applications in the geometry of Riemannian submanifolds and…

This paper studies modular forms of rank four and level one. There are two possiblities for the isomorphism type of the space of modular forms that can arise from an irreducible representation of the modular group of rank four, and we…

Let $F$ be a local field of mixed characteristic, let $k$ be a finite extension of its residue field, let ${\mathcal H}$ be the pro-$p$-Iwahori Hecke $k$-algebra attached to ${\rm GL}_{d+1}(F)$ for some $d\ge1$. We construct an exact and…

We give a method of representing the modular invariant function by generators of a modular function field.

The main subject of this work is the difference between the coarse moduli space and the stack of hyperelliptic curves. We compute their Picard groups, giving explicit description of the generators. We get an application to the…

We extend methods of Greenberg and the author to compute in the cohomology of a Shimura curve defined over a totally real field with arbitrary class number. Via the Jacquet-Langlands correspondence, we thereby compute systems of Hecke…

Although links between values of finite field hypergeometric functions and eigenvalues of elliptic modular forms are well known, we establish in this paper that there are also connections to eigenvalues of Siegel modular forms of higher…

In this paper we classify and give Kazhdan-Lusztig type character formulas for equivariantly irreducible representations of Lie algebras of reductive algebraic groups over a field of large positive characteristic. The equivariance is with…

Generalising the recent method of Andreatta, Iovita, and Pilloni for cuspidal forms, we construct an eigenvariety for symplectic and unitary groups that parametrises systems of eigenvalues of overconvergent and locally analytic $p$-adic…

For a positive integer $N$ divisible by $4,5,6,7$ or $9$, let $\mathcal{O}_{1,N}(\mathbb{Q})$ be the ring of weakly holomorphic modular functions for the congruence subgroup $\Gamma_1(N)$ with rational Fourier coefficients. We present…

In this article we show that 'most' of the vector valued modular forms w.r.t. the Weil representation on the groups rings $\mathbb{C}[D]$ of discriminant forms D are oldforms. The precise meaning of oldform is that the form can be…

Let $p$ be a prime number, $F$ a field of characteristic $p$, and $G$ a cyclic group of order $q =p^a$ for some positive integer $a$. Under these circumstances every indecomposable $F G$-module is cyclic. For indecomposable $F G$-modules…

Matrix representations of Hecke operators on classical holomorphical cusp forms and corresponding period polynomials are well known. In this article we define Hecke operators on period functions and show that they correspond to the Hecke…

This paper describes the module categories for a family of generic Hecke algebras that specialize to the complex reflection groups G(r,1,n) and to the certain endomorphism rings of permutation characters of finite general linear groups. In…

We find some modularity criterion for a product of Klein forms of the congruence subgroup $\Gamma_1(N)$ and, as its application, construct a basis of the space of modular forms for $\Gamma_1(13)$ of weight $2$. In the process we face with…

This paper considers generators of Heisenberg modules in the case of twisted group $C^*$-algebras of closed subgroups of locally compact abelian groups and how the restrction and/or periodization of these generators yield generators for…

In this paper, we study the Drinfeld cusp forms for $\Gamma_1(T)$ and $\Gamma(T)$ using Teitelbaum's interpretation as harmonic cocycles. We obtain explicit eigenvalues of Hecke operators associated to degree one prime ideals acting on the…

In this paper, we study congruences of Hecke eigenvalues between Hermitian Klingen-Eisenstein series and cusp forms on the unitary group $\mathrm{U}_{n,n}$ defined over the rational number field $\mathbb{Q}$. We also prove the rationality…

We classify Siegel modular cusp forms of weight two for the paramodular group K(p) for primes p< 600. We find that weight two Hecke eigenforms beyond the Gritsenko lifts correspond to certain abelian varieties defined over the rationals of…