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Zeta functions of finite fields and the Selberg class

Volume 184 / 2018

J. Kaczorowski, A. Perelli Acta Arithmetica 184 (2018), 247-265 MSC: 11M41, 11G20, 11G25. DOI: 10.4064/aa170811-12-1 Published online: 26 July 2018


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 $\mathcal S_0^\sharp$, we first describe how to associate suitable local $L$-functions from $\mathcal S^\sharp_0$ to the varieties over a finite field. Then we show that, in a suitable sense and under a certain hypothesis, $\mathcal S_0^\sharp$ is generated by the local $L$-functions coming from curves.


  • J. KaczorowskiFaculty of Mathematics and Computer Science
    A. Mickiewicz University
    61-614 Poznań, Poland
    Institute of Mathematics
    Polish Academy of Sciences
    00-656 Warszawa, Poland
  • A. PerelliDipartimento di Matematica
    Università di Genova
    via Dodecaneso 35
    16146 Genova, Italy

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