Values of zeta functions at s=1/2
arXiv:math/0502507 · doi:10.1155/IMRN.2005.1519
Abstract
We study the behaviour near s=1/2 of zeta functions of varieties over finite fields F_q with q a square. The main result is an Euler-characteristic formula for the square of the special value at s=1/2. The Euler-characteristic is constructed from the Weil-etale cohomology of a certain supersingular elliptic curve.
Submitted version. IMRN (to appear)