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On the <f>p</f>-adic Riemann hypothesis for the zeta function of divisors
- Source :
-
Journal of Number Theory . Feb2004, Vol. 104 Issue 2, p335. 18p. - Publication Year :
- 2004
-
Abstract
- In this paper, we continue the investigation of the zeta function of divisors, as introduced by the first author in Wan (in: D. Jungnickel, H. Niederreiter (Eds.), Finite Fields and Applications, Springer, Berlin, 2001, pp. 437–461; Manuscripta Math. 74 (1992) 413), for a projective variety over a finite field. Assuming that the set of effective divisors in the divisor class group forms a finitely generated monoid, then there are four conjectures about this zeta function: <f>p</f>-adic meromorphic continuation, rank and pole relation, <f>p</f>-adic Riemann hypothesis, and simplicity of zeros and poles. This paper proves all four conjectures when the Chow the group of divisors is of rank one. Also, an example with higher rank is provided where all four conjectures hold. [Copyright &y& Elsevier]
- Subjects :
- *ZETA functions
*NEWTON diagrams
*MEROMORPHIC functions
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 0022314X
- Volume :
- 104
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 11886440
- Full Text :
- https://doi.org/10.1016/j.jnt.2003.08.008