Arithmetic of characteristic p special L-values
نویسندگان
چکیده
منابع مشابه
Special Values of L-functions and the Arithmetic of Darmon Points
Building on our previous work on rigid analytic uniformizations, we introduce Darmon points on Jacobians of Shimura curves attached to quaternion algebras over Q and formulate conjectures about their rationality properties. Moreover, if K is a real quadratic field, E is an elliptic curve over Q without complex multiplication and χ is a ring class character such that LK(E,χ, 1) 6= 0 we prove a G...
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The purpose of the paper is to extend and refine earlier results of the author on nonvanishing of the L-functions associated to modular forms in the anticyclotomic tower of conductor p over an imaginary quadratic field. While the author’s previous work proved that such L-functions are generically nonzero at the center of the critical strip, provided that the sign in the functional equation is +...
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We present an algorithm to compute values L(s) and derivatives L(s) of L-functions of motivic origin numerically to required accuracy. Specifically, the method applies to any L-series whose Γ-factor is of the form A ∏d i=1 Γ( s+λj 2 ) with d arbitrary and complex λj , not necessarily distinct. The algorithm relies on the known (or conjectural) functional equation for L(s).
متن کاملPeriods and Special Values of L-functions
Introduction 1 1. Modular forms, congruences and the adjoint L-function 2 2. Quaternion algebras and the Jacquet-Langlands correspondence 6 3. Integral period relations for quaternion algebras over Q 8 4. The theta correspondence 12 5. Arithmetic of the Shimizu lift and Waldspurger’s formula 16 6. Hilbert modular forms, Shimura’s conjecture and a refined version 19 7. Unitary groups and Harris’...
متن کاملRemarks on special values of L-functions
This article does not represent precisely a talk given at the symposium, but is complementary to [DenS]. Its purpose is to explain a setting in which the various conjectures on special values of L-functions admit a unified formulation. At critical points, Deligne’s conjecture [Del2] relates the value of an L-function to a certain period, and at non-critical points, the conjectures of Beilinson ...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2015
ISSN: 0024-6115
DOI: 10.1112/plms/pdu067