Spinor zeta functions at the central point
by
Winfried Kohnen
Universität Heidelberg, Mathematisches Institut, Heidelberg, Germany

According to Waldsburger (1981), under certain conditions the central critical values of the Hecke L-function of a normalized elliptic newform f of even integral weight twisted with quadratic characters are proportional to the squares of the Fourier coefficients of a modular form of half-integral weight g corresponding to f under the Shimura correspondence. In 1986 S. Boecherer made a conjecture according to which the central values of the spinor zeta function of a Siegel-Hecke eigenform f of genus 2 twisted with odd quadratic characters should be related to the squares of a sum of certain of the Fourier coefficients of f. This conjecture so far is unproved.

In my talk I would like to discuss Boecherer's conjecture in some detail and provide some numerical examples supporting it (joint work with M. Kuss, 1999).

Date received: April 19, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacf-36.