Values of zeta functions at s=1/2

Details Values of zeta functions at s=1/2 Values of zeta functions at s=1/2

2005-02-24

arxiv.org/abs/math/0502507v2

Mathematics

Number Theory

Submitted version. IMRN (to appear)

Scientific paper

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.

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