Special values of the elliptic modular function and factorization formulae.
Stickelberger Ideals.
Subgroups of the (2,3,7) Triangle Group.
Subgroups of the modular group defined by a single linear congruence
Sur la nature arithmétique des valeurs de fonctions modulaires
Sur la recherche des -extensions non ramifiées de
Sur le développement des fonctions de M. Weierstrass suivant les puissances croissantes de la variable.
Sur l'équation linéaire qui relie au module la fonction complète de première espèce
The Action of the Canonical Involution on Modular Forms of Weight 2 on ...0 (M).
The constant term of the cubic theta series.
The Equations for Modular Function Fields of Principal congruence subgroups of prime level.
The Group of Automorphisms of the Modular Function Field.
The Index of Stickelberger Ideals of Order2 and Cuspidal Class Numbers .
The laplacian operator on a Riemann surface
The laplacian operator on a Riemann surface, II
The laplacian operator on a Riemann surface, III
The Lax-Phillips infinitesimal generator and the scattering matrix for automorphic functions
We study the infinitesimal generator of the Lax-Phillips semigroup of the automorphic scattering system defined on the Poincaré upper half-plane for SL₂(ℤ). We show that its spectrum consists only of the poles of the resolvent of the generator, and coincides with the poles of the scattering matrix, counted with multiplicities. Using this we construct an operator whose eigenvalues, counted with algebraic multiplicities (i.e. dimensions of generalized eigenspaces), are precisely the non-trivial zeros...
The logarithm of the Siegel function
The module of vector-valued modular forms is Cohen-Macaulay
Let denote a finite index subgroup of the modular group and let denote a finite-dimensional complex representation of Let denote the collection of holomorphic vector-valued modular forms for and let denote the collection of modular forms on . Then is a -graded -module. It has been proven that may not be projective as a -module. We prove that is Cohen-Macaulay as a -module. We also explain how to apply this result to prove that if is a polynomial ring, then is a free...
The polynomial and elliptic curves of conductor 11