Average L-values, class numbers and special points -- Dinakar Ramakrishnan (Caltech), March 22, 2005

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Let K = \Q(\sqrt{D}) be an imaginary quadratic field of
discriminant D<0. A fundamental invariant of K is the class number h_D,
which was introduced by Gauss in his study of integral, binary quadratic
forms of discriminant D. After reviewing certain known results and questions
concerning h_D, we will discuss a formula, established in joint work with
Philippe Michel, relating h_D to certain averages of central L-values of
cusp forms of weight 2. There will be no proofs, and the emphasis will be on
explaining the formula and some consequences.