Explicit Estimates in the Arithmetic Theory of Cusp Forms and Poincaré Series.
Expressing a number as the sum of two coprime squares.
We use hyperbolic geometry to study the limiting behavior of the average number of ways of expressing a number as the sum of two coprime squares. An alternative viewpoint using analytic number theory is also given.
Facteurs -simples de de grande dimension et de grand rang
Families of modular forms
We give a down-to-earth introduction to the theory of families of modular forms, and discuss elementary proofs of results suggesting that modular forms come in families.
Finite Groups and Hecke Operators.
Fonctions modulaires, courbes de Tate et indépendance algébrique
Forces modulaires à une et deux variables
Formes modulaires et nombres de Ramanujan
Fourier coefficients of cusp forms and the Riemann zeta-function
Fourier coefficients of real analytic cusp forms of arbitrary real weight
Fractional integrals of modular forms
Galois representations, embedding problems and modular forms.
To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective representations...
Galois representations into GL2(Zp[[X]]) attached to ordinary cusp forms.
Gauss Sums and Elliptic Functions: II. The Quartic Sum.
Gauss's ₂F₁ hypergeometric function and the congruent number elliptic curve
Generalized modular forms representable as eta products
Generation of class fields by the modular function
Generation of Hauptmoduln of Γ1(N) by Weierstrass units and application to class fields
We show that the modular functions j 1,N generate function fields of the modular curve X 1(N), N ∈ {7; 8; 9; 10; 12}, and apply them to construct ray class fields over imaginary quadratic fields.
Generators and equations for modular function fields of principal congruence subgroups
Hecke operators and Lambert series.