IJPAM: Volume 63, No. 3 (2010)

NOTES ON THE RIEMANN HYPOTHESIS
IN CHARACTERISTIC $p$

Víctor Bautista-Ancona$^1$, Javier Diaz-Vargas$^2$, Gabriel Villa-Salvador$^3$
$^{1,3}$Departamento de Control Automático
Centro de Investigación y de Estudios Avanzados del I.P.N.
Apartado Postal 14-740, México, D.F., 07000, MÉXICO
$^1$e-mail: [email protected]
$^3$e-mail: [email protected]
$^2$Facultad de Matemáticas
Universidad Autónoma de Yucatán
Periférico Norte Tablaje, 13615, Cordemex
Mérida, Yucatán, 97110, MÉXICO
e-mail: [email protected]


Abstract.In this paper we give a full view on the proof of Riemann's Hypothesis for Goss zeta function in characteristic $p>0$. First, we present the set up of the problem. Then, we analyze the proof of J. Diaz-Vargas for the $q=p$ case. Next, we discuss the main ideas of the unpublished note of B. Poonen for the case $q=4$ from a combinatorial point of view and how this ideas cannot be extended to more general cases. Finally we give an overview on how J. Sheats proves the general case.

Received: July 9, 2010

AMS Subject Classification: 11R58, 11G09, 11M41

Key Words and Phrases: Goss zeta function, Carlitz zeta function, Riemann Hypothesis in positive characteristic

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 63
Issue: 3