Related papers: Symmetric power functoriality for holomorphic modu…

We define canonical real analytic versions of modular forms of integral weight for the full modular group, generalising real analytic Eisenstein series. They are harmonic Maass waveforms with poles at the cusp, whose Fourier coefficients…

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 prove a power saving over the trivial bound for the number of cohomological cuspidal automorphic representations of fixed level and growing weight on $GL_3/\mathbb{Q}$, by adapting the methods of our earlier paper on $GL_2$.

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 $\mathrm{E}_8\oplus \mathrm{A}_1$,…

In this work we construct an eigencurve for p-adic modular forms attached to an indefinite quaternion algebra over Q. Our theory includes the definition, both as rules on test objects and sections of line bundle, of p-adic modular forms,…

Let F be a real quadratic field with ring of integers O and with class number 1. Let Gamma be a congruence subgroup of GL_2 (O). We describe a technique to compute the action of the Hecke operators on the cohomology H^3 (Gamma; C). For F…

In this paper we prove the homotopy lifting property for symmetric products $SP_{m}(X)$ and $F_{m}(X)$, with $X$ a Hausdorff topological space. Furthermore, we introduce a new tool, the theory of topological puzzles, to get a useful…

This paper is a continuation of the author's previous wotk. We supplement four results on a family of holomorphic Siegel cusp forms for $GSp_4/\mathbb{Q}$. First, we improve the result on Hecke fields. Namely, we prove that the degree of…

We show that the systems of prime-to-$p$ Hecke eigenvalues arising from automorphic forms$\pmod p$ for a good prime $p$ associated to an algebraic group $G/\mathbb Q$ of Hodge type are the same as those arising from algebraic modular…

We prove various results on the cohomology of arithmetic lattices arising from quaternion algebras over a number field with at least one complex place, including a strong restriction on the allowable weights of cuspidal cohomological…

We report on a computation of holomorphic cuspidal modular forms of weight one and small level (currently level at most $1500$) and classification of them according to the projective image of their attached Artin representations. The data…

We study monodromy of holomorphic motions and show the equivalence of triviality of monodromy of holomorphic motions and extensions of holomorphic motions to continuous motions of the Riemann sphere. We also study liftings of holomorphic…

Poincare-type series, such as Selberg's, are known to produce automorphic functions, in the hyperbolic half-plane, the decompositions of which into eigenfunctions (genuine or generalized) of the automorphic Laplacian contain all modular…

It is shown that each complex conjugate of a meromorphic modular form for $\mathrm{SL}_2(\mathbb{Z})$ of any complex weight $p$ occurs as the image of a harmonic modular form under the operator $2i y^p \, \partial_{\bar z}$. These harmonic…

In this article we prove level raising for cuspidal eigenforms modulo prime powers (for odd primes) of weight $k\geq 2$ and arbitrary character, extending the result in weight two established by the work of Tsaknias and Wiese and…

In this paper, we prove that the Hecke eigenvalue square for a holomorphic cusp form and the Piltz divisor functions are good weighting functions for the pointwise ergodic theorem. This partially solves problems suggested by Cuny and Weber.…

We establish a structure theorem for the connected automorphism groups of smooth complete toroidal horospherical varieties, that is, toric fibrations over rational homogeneous spaces. The key ingredient is a characterization of the Demazure…

Motivated by the work of of A. Zelevinsky on positive self-adjoint Hopf algebras, we define what we call a symmetric self-adjoint Hopf structure for a certain kind of semisimple abelian categories. It is known that every positive…

This is a semi-expository article concerning Langlands functoriality and Deligne's conjecture on the special values of $L$-functions. The emphasis is on symmetric power $L$-functions associated to a holomorphic cusp form, while appealing to…

In this paper we establish a new case of Langlands functoriality. More precisely, we prove that the tensor product of the compatible system of Galois representations attached to a level-1 classical modular form and the compatible system…