We analyze the relations between the zeta functions of smooth projective varieties over finite fields and the functions of degree $0$ from the extended Selberg class. In particular, denoting such functions by $S_0^sharp$, we first describe how to associate suitable local $L$-functions from $S^sharp_0$ to the varieties over a finite field. Then we show that, in a suitable sense and under a certain hypothesis, $S_0^sharp$ is generated by the local $L$-functions coming from curves.

Zeta functions of finite fields and the Selberg class

PERELLI, A.
2018

Abstract

We analyze the relations between the zeta functions of smooth projective varieties over finite fields and the functions of degree $0$ from the extended Selberg class. In particular, denoting such functions by $S_0^sharp$, we first describe how to associate suitable local $L$-functions from $S^sharp_0$ to the varieties over a finite field. Then we show that, in a suitable sense and under a certain hypothesis, $S_0^sharp$ is generated by the local $L$-functions coming from curves.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11567/887500
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