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 F_q[T]", Journal of Number Theory, 71 (1): 121–157, arXiv:math/9801158, doi:10.1006/jnth.1998.2232, ISSN 0022-314X, MR 1630979