In this paper we prove a nonvanishing theorem for central values of L– functions associated to a large class of algebraic Hecke characters of CM number fields. A key ingredient in the proof is an asymptotic formula for the average of these central values. We combine the nonvanishing theorem with work of Tian and Zhang [TZ] to deduce that infinitely many of the CM abelian varieties associated to...

Using first principles, it is demonstrated that radiative damping alone cannot lead to a nonvanishing linear electro-optic effect in a chiral isotropic medium. This conclusion is in contrast with that obtained by a calculation in which damping effects are included using the standard phenomenological model. We show that these predictions differ because the phenomenological damping equations are ...

2.1. The Cebotarev density theorem. We have seen in the proof of Theorem 1.3 that for any nontrivial ray class character χ : H → C× we could show nonvanishing L(1, χ) = 0 provided that χ factors through J/NL/KJ L · P for some finite extension L/K. By Theorem 1.2 the subgroup P is the norm subgroup of the ray class field K(m)/K. Hence we get nonvanishing for all nontrivial χ and this allows to p...

Using first principles, it is demonstrated that radiative damping alone cannot lead to a nonvanishing electro-optic effect in a chiral isotropic medium. This conclusion is in contrast with that obtained by a calculation in which damping effects are included using the standard phenomenological model. We show that these predictions differ because the phenomenological damping equations are valid o...

S O u {1} is a compact subset of A. Duren and Schober had been interested in extreme points and support points of S o. Recall that a support point of a family F is a function which maximizes the real part of some continuous linear functional, that is not constant over F. We shall give a characterization of the extreme points and support points of the subfamily So(R ) of nonvanishing univalent f...

The minimal area covered by the image of the unit disk is found for nonvanishing univalent functions normalized by the conditions f(0) = 1, f ′(0) = α. Two different approaches are discussed, each of which contributes to the complete solution of the problem. The first approach reduces the problem, via symmetrization, to the class of typically real functions, where the well-known integral repres...