Rings of Hilbert modular forms

—The existence and construction of vector-valued modular forms (vvmf) for any arbitrary Fuchsian group G, for any representation ρ : G −→ GL d ( C ) of finite image can be

— Modular forms modulo p, imaginary quadratic fields, Hecke operators, Serre weight.... This fact has some

We prove that oeients of q -expansions of modular forms an be omputed in polynomial time under ertain assumptions, the most important of whih is the Riemann.. hypothesis for ζ

– We prove non-trivial lower bounds for the growth of ranks of Selmer groups of Hilbert modular forms over ring class fields and over certain Kummer extensions, by establishing first

In the case of forms corresponding to (modular) elliptic curves, results relating the value to certain Galois cohomology groups (Selmer groups) were obtained by Coates and Schmidt

The main technique is a motivic variation of theorems of Mazur, Ogus, Illusie and Nygaard on the Katz conjecture (according to which the Newton polygon of Frobenius on

Toute utilisa- tion commerciale ou impression systématique est constitutive d’une in- fraction pénale. Toute copie ou impression de ce fichier doit conte- nir la présente mention

In section 5, we make use of the Rankin-Selberg integral representation derived by Im [I] to prove the algebraicity of the distribution, and we can verify this via the