Goss zeta function

In mathematics, the Goss zeta function, named after David Goss, is an analogue of the Riemann zeta function for function fields. Sheats proved that it satisfies an analogue of the Riemann hypothesis. Kapranov proved results for a higher-dimensional generalization of the Goss zeta function.

References

Sources

• Goss, David (1996). Basic Structures of Function Field Arithmetic. A Series of Modern Surveys in Mathematics. Vol. 35. Berlin, Heidelberg: Springer. ISBN 978-3-540-61087-8. MR 1423131.

• Kapranov, M. (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. doi:10.1006/jnth.1998.2232. MR 1630979.

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