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Values of zeta functions at s=1/2

Niranjan Ramachandran
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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.

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Niranjan Ramachandran. 2005-02-24. Values of zeta functions at s=1/2. https://doi.org/10.1155/imrn.2005.1519

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