Related papers: A Generalization of Level-Raising Congruences for …

In this paper we first prove an isomorphism between certain spaces of Jacobi forms. Using this isomorphism, we study the mod $p$ theory of Hermitian Jacobi forms over $\mathbb{Q}(i)$. We then apply the mod $p$ theory of Hermitian Jacobi…

In this paper we discuss the existence of certain classes of cuspidal automorphic representations having non-zero Fourier coefficients for general semisimple algebraic group $G$ defined over a number field $k$ such that its Archimedean…

First we explain the concept of local deformation over a 'parameter' algebra P, in particular the notion of a P-lattice in a Lie group. Purpose of this article is to define the spaces of automorphic resp. cusp forms on the upper half plane…

We prove an automatic convergence theorem for holomorphic modular forms on tube domains. The argument works in some generality, and covers in particular the case of orthogonal groups, symplectic groups, unitary and quaternion unitary…

We determine conditions for the existence and non-existence of Ramanujan-type congruences for Jacobi forms. We extend these results to Siegel modular forms of degree 2 and as an application, we establish Ramanujan-type congruences for…

In this paper we give an example of a noncongruence subgroup whose three-dimensional space of cusp forms of weight 3 has the following properties. For each of the four residue classes of odd primes modulo 8 there is a basis whose Fourier…

We study the geometry of the $p$-adic Siegel eigenvariety $\mathcal{E}$ of paramodular tame level at certain Saito-Kurokawa points having a critical slope. For $k \geq 2$ let $f$ be a cuspidal new eigenform of…

We attempt to generalize a congruence property of elliptic modular forms proved by Sturm to that of Haupttypus of Siegel modular forms of degree 2 with level. Namely, we give an explicit bound of Fourier coefficients required to determine…

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…

We prove the conjecture of Pollack and Weston on the quantitative analysis of the level lowering congruence \`{a} la Ribet for modular forms of higher weight. It was formulated and studied in the context of the integral Jacquet-Langlands…

Let p>2 be a rational prime, k be a perfect field of characteristic p and K be a finite totally ramified extension of the fractional field of the Witt ring of k. Let G and H be finite flat commutative group schemes killed by p over O_K and…

In this paper we will use experimental and computational methods to find modular forms for non-congruence subgroups, and the modular forms for congruence subgroups that they are associated with via the Atkin--Swinnerton-Dyer correspondence.…

We prove a formula (analogous to that of Kida in classical Iwasawa theory and generalizing that of Hachimori-Matsuno for elliptic curves) giving the analytic and algebraic p-adic Iwasawa invariants of a modular eigenform over an abelian…

We prove a degree-one saving bound for the dimension of the space of cohomological automorphic forms of fixed level and growing weight on $\mathrm{SL}_2$ over any number field that is not totally real. In particular, we establish a sharp…

Let k be an algebraically closed field of characteristic zero, F its algebraically closed extension, and G be the group of k-automorphisms of F endowed with a natural topology. One of the purposes of this paper is to show that any…

We prove in this paper a classicality result for overconvergent modular forms on PEL Shimura varieties of type (A) or (C), without any ramification hypothesis. We use an analytic continuation method, which generalizes previous results in…

We introduce and study certain hyperbolic versions of automorphic Lie algebras related to the modular group. Let $\Gamma$ be a finite index subgroup of $\mathrm{SL}(2,\mathbb{Z})$ with an action on a complex simple Lie algebra $\mathfrak…

We study a notion of cusp forms for the symmetric spaces G/H with G = SL(n,R) and H = S(GL(n-1,R) x GL(1,R)). We classify all minimal parabolic subgroups of G for which the associated cuspidal integrals are convergent and discuss the…

This paper is lead by the question whether there is a nice structure theory of finitely generated modules over the Iwasawa algebra, i.e. the completed group algebra, R of a p-adic analytic group G. For G without any p-torsion element we…

Let $G$ be a finite non-abelian $p$-group, where $p$ is a prime. Let $\mathrm{Aut}_c(G)$ and $\mathrm{Aut}_z(G)$ respectively denote the group of all class preserving and central automorphisms of $G$. We give a necessary condition for $G$…