EXPLICIT METHODS FOR HILBERT MODULAR FORMS LASSINA DEMB´EL´E AND JOHN VOIGHT Abstract.

—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

This generalization, performed for p-ad- missible primes, is used by the author in [L2] to prove the Birch and Swinnerton-Dyer conjecture for modular elliptic curves E with every-

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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

The first will be results on “domains of automatic analytic continuation” for overconvergent Hilbert modular forms as in [Kas13, KST12], where no slope conditions are given (apart

– 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

The induction step, in the case of binary theta functions, is provided by Theorem 4.7 of Part I, which in turn is based on my joint work.. with Kudla on

HIRZEBRUCH: The ring of Hilbert modular forms for real quadratic number fields of small discriminant, Lecture Notes in Math.. PRESTEL: Die elliptische Fixpunte