Related papers: Symmetric power functoriality for holomorphic modu…

Let G be a semisimple Lie group with no compact factors, K a maximal compact subgroup of G, and $\Gamma$ a lattice in G. We study automorphic forms for $\Gamma$ if G is of real rank one with some additional assumptions, using dynamical…

Given two semistable, non potentially isotrivial elliptic surfaces over a curve $C$ defined over a field of characteristic zero or finitely generated over its prime field, we show that any compatible family of effective isometries of the…

Extending well-known results on surfaces, we give bounds on the cohomological action of automorphisms of compact K\"ahler threefolds. More precisely, if the action is virtually unipotent we prove that the norm of $(f^n)^*$ grows at most as…

Let $d$ be a positive fundamental discriminant, and let $\mathcal{C}_{d}$ be the set of isomorphism classes of cubic number fields of discriminant $d$. For each $K \in \mathcal{C}_{d}$, we construct a weight 1 modular form $f_{K}$ with…

We compute the quantum variance of holomorphic cusp forms on the vertical geodesic for smooth compactly supported test functions. As an application we show that almost all holomorphic Hecke cusp forms, whose weights are in a short interval,…

In this article, we establish an asymptotic estimate on the number of cuspidal automorphic representations of ${\rm GL}_4(\mathbb A_{\mathbb Q})$ which contribute to the cuspidal cohomology of ${\rm GL}_4$ and are obtained from symmetric…

We introduce and begin to analyse a class of algebras, associated to congruence subgroups, that extend both the algebra of modular forms of all levels and the ring of classical Hecke operators. At the intuitive level, these are algebras of…

We extend a well-known result, about the unit ball, by H. Alexander to a class of balanced domains in $\mathbb{C}^n, \ n > 1$. Specifically: we prove that any proper holomorphic self-map of a certain type of balanced, finite-type domain in…

The symmetric homology of a unital algebra $A$ over a commutative ground ring $k$ is defined using derived functors and the symmetric bar construction of Fiedorowicz. For a group ring $A = k[\Gamma]$, the symmetric homology is related to…

In this paper we prove two new cases of Langlands functoriality. The first is a functorial product for cusp forms on $GL_2\times GL_3$ as automorphic forms on $GL_6$, from which we obtain our second case, the long awaited functorial…

There is a lifting from a non-CM elliptic curve $E/\mathbb{Q}$ to a paramodular form $f$ of degree $2$ and weight $3$ given by the symmetric cube map. We find the level of $f$ in an explicit way in terms of the coefficients of the…

We determine the number of level 1, polarized, algebraic regular, cuspidal automorphic representations of GL_n over Q of any given infinitesimal character, for essentially all n <= 8. For this, we compute the dimensions of spaces of level 1…

E(2) is studied as the automorphism group of the Heisenberg algebra H. The basis in the Hilbert space K of functions on H on which the unitary irreducible representations of the group are realized is explicitely constructed. The addition…

In this paper, we study the average of the Fourier coefficients of a holomorphic cusp form for the full modular group at primes of the form $[g(n)]$.

If $f$ is a mod-$3$ eigenform of weight 2 and level $\Gamma_0(\ell^2)$ for a prime $\ell$ such that $\ell \equiv -1 \pmod{3}$, and $\ell$ is a vexing prime for $f$, we show that there is no obstruction to finding a minimal lift of $f$, but…

We give a criterium of holomorphy for some type formal power series. This gives a stronger form of a Rothstein's type extension theorem for a particular ring of holomorphic functions.

We prove an integrality result for the value at s=1 of the adjoint L-function associated to a cohomological cuspidal automorphic representation on GL(n) over any number field. We then show that primes (outside an exceptional set) dividing…

Let $q$ be a prime power and $\mathbb{F}_q$ be the finite field with $q$ elements. In this article we investigate the space of unramified automorphic forms for $\mathrm{PGL}_n$ over the rational function field defined over $\mathbb{F}_q$…

The object of this work is the spinor L-function of degree 3 and certain degeneration related to the functoriality principle. We study liftings of automorphic forms on the pair of symplectic groups $(\text{GSp}(2),\text{GSp}(4))$ to…

The classical Maass lift is a map from holomorphic Jacobi forms to holomorphic scalar-valued Siegel modular forms. Automorphic representation theory predicts a non-holomorphic and vector-valued analogue for Hecke eigenforms. This paper is…