Analyse spectrale et prolongement analytique : séries d’Eisenstein, fonctions et nombre de solutions d’équations diophantiennes
Analytic continuation of representations and estimates of automorphic forms.
Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan.
Andrianov' s L-functions associated to Siegel wave forms of degree two.
Announcement of errors in "The Eichler Commutation Relation for theta series with spherical harmonics" (Acta Arith. 63 (1993), 233-254)
Annulation de la cohomologie cuspidale de sous-groupes de congruence de GL...(...).
Anti-cyclotomic Katz -adic -functions and congruence modules
Anticyclotomic main conjectures.
Appendix: A refinement of the strong multiplicity one theorem for GL(2). (Appendix to R. Taylor).
Appendix to Orloff: Critical values of certain tensor product L-functions.
Applications of special functions for the general linear group to number theory
Approximative Funktionalgleichungen und Mittelwertsätze für Dirichletreihen, die Spitzenformen assoziiert sind.
Arithmetic cycles on Picard modular surfaces and modular forms of Nebentypus.
Arithmetic differential equations in several variables
We survey recent work on arithmetic analogues of ordinary and partial differential equations.
Arithmetic Fuchsian groups and the number of systoles.
Arithmetic Hilbert modular functions (II).
The purpose of this paper, which is a continuation of [2, 3], is to prove further results about arithmetic modular forms and functions. In particular we shall demonstrate here a q-expansion principle which will be useful in proving a reciprocity law for special values of arithmetic Hilbert modular functions, of which the classical results on complex multiplication are a special case. The main feature of our treatment is, perhaps, its independence of the theory of abelian varieties.
Arithmetic of certain hypergeometric modular forms
Arithmetic of half integral weight theta-series
Arithmetic of the modular function
We find a generator of the function field on the modular curve X₁(4) by means of classical theta functions θ₂ and θ₃, and estimate the normalized generator which becomes the Thompson series of type 4C. With these modular functions we investigate some number theoretic properties.
Arithmetic vector bundles and automorphic forms on Shimura vartieties. I.