منابع مشابه
Special Values of Abelian L - Functions at S = 0
In [12], Stark formulated his far-reaching refined conjecture on the first derivative of abelian (imprimitive) L–functions of order of vanishing r = 1 at s = 0. In [10], Rubin extended Stark’s refined conjecture to describe the r-th derivative of abelian (imprimitive) L-functions of order of vanishing r at s = 0, for arbitrary values r. However, in both Stark’s and Rubin’s setups, the order of ...
متن کاملSpecial Values of Anticyclotomic L-functions
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 +...
متن کاملComputing Special Values of Motivic L-Functions
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 ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2015
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2014.07.012