Room 70A, Ross Building, Jerusalem, Israel
Let L(E/Q, s) be the L-function of an elliptic curve E defined over the rational field Q. We examine the central value L(E, 1, χ) of twists of L(E/Q, s) by Dirichlet characters χ. We discuss the vanishing and non-vanishing frequencies of these values as χ ranges over characters of fixed order greater than 2. We also examine thee square-free part of the algebraic part of L(E/F, 1) for abelian fields F/Q when these values are non-zero.