In the field of mathematics, the Goss zeta function, named after David Goss, is an analogue of the Riemann zeta function for function fields. Sheats (1998) proved that it satisfies an analogue of the Riemann hypothesis. Kapranov (1995) proved results for a higher-dimensional generalization of the Goss zeta function.
References Goss, David (1996), Basic structures of function field arithmetic, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 35, Berlin, New York: Springer-Verlag, ISBN 978-3-540-61087-8, MR 1423131 Kapranov, Mikhail (1995), "A higher-dimensional generalization of the Goss zeta function", Journal of Number Theory, 50 (2): 363–375, doi:10.1006/jnth.1995.1030 Sheats, Jeffrey T. (1998), "The Riemann hypothesis for the Goss zeta function for Fq[T]", Journal of Number Theory, 71 (1): 121–157, arXiv:math/9801158, doi:10.1006/jnth.1998.2232, ISSN 0022-314X, MR 1630979