We compute the number of F_q-points on M_4,n for n≤3 and show that it is a polynomial in
q, using a sieve based on Hasse--Weil zeta functions. As an application, we prove that the …

We give an explicit conjectural formula for the motivic Euler characteristic of an arbitrary
symplectic local system on the moduli space A _3 of principally polarized abelian threefolds …

Let G be a special orthogonal group or an inner form of a symplectic group over a number
field F such that there exists a non-empty set S of real places of F at which G has discrete …

We show how one can use the representation theory of ternary quartics to construct all
vector-valued Siegel modular forms and Teichmüller modular forms of degree 3. The …

Soit G= G (ℝ) le groupe des points réels d'un groupe algébrique connexe réductif quasi-
déployé défini sur ℝ. Supposons de plus que G soit un groupe classique (symplectique …

We use a classification result of Chenevier and Lannes for algebraic automorphic
representations together with a conjectural correspondence with ℓ-adic absolute Galois …

We prove that the rational cohomology group and its image under Gysin push-forward for
tautological maps to produce many new examples of moduli spaces of stable curves with …

The aim of this paper is twofold. First, we introduce a new method for evaluating the
multiplicity of a given discrete series representation in the space of level 1 automorphic …

We prove the existence of a regular algebraic cuspidal automorphic representation $\pi $ for
$ GL_ {105}/\mathbf {Q} $ of level one and weight zero. We construct $\pi $ using symmetric …

In this survey note we present an approach to the generalization of Serre of the Sato-Tate
Conjecture. The reader interested in a complete account is referred to Serre's original …