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Results tagged with l-functions
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user 91041
Questions about generalizations of the Riemann Zeta function of arithmetic interest whose definition relies on meromorphic continuation of special kinds of Dirichlet series, such as Dirichlet L-functions, Artin L-functions, elements of the Selberg class, automorphic L-functions, Shimizu L-functions, p-adic L-functions, etc.
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Zeta function of variety over positive characteristic function field vs. local zeta factor o...
Let $X = Y \times_{\mathbb{F}_q} C$, with $Y, C / \mathbb{F}_q$ smooth projective varieties, $C$ a curve. Let $d = \dim_{\mathbb{F}_q} X$. We can consider the local zeta function $Z(X, t) = \prod\limi …
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Zeta function of variety over positive characteristic function field vs. local zeta factor o...
The two zeta functions are the same. This is an immediate corollary of Milne, Etale Cohomology, proposition 13.8(c).
Reference:
Milne, J. S. Etale Cohomology (PMS-33). Princeton University Press, 1980 …
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