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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Titolo: | Zeta functions of finite fields and the Selberg class |
Autori: | |
Data di pubblicazione: | 2018 |
Rivista: | |
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. |
Handle: | http://hdl.handle.net/11567/887500 |
Appare nelle tipologie: | 01.01 - Articolo su rivista |
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