Rank one case of Dwork’s conjecture
Author:
Daqing Wan
Journal:
J. Amer. Math. Soc. 13 (2000), 853-908
MSC (2000):
Primary 11G40, 11S40; Secondary 11M41, 11G25
DOI:
https://doi.org/10.1090/S0894-0347-00-00340-4
Published electronically:
June 6, 2000
MathSciNet review:
1775761
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: In this paper, we prove the rank one case of Dwork’s conjecture on the $p$-adic meromorphic continuation of the pure slope L-functions arising from the slope decomposition of an overconvergent F-crystal. Further explicit information about zeros and poles of the pure slope L-functions are also obtained, including an application to the Gouvêa-Mazur type conjecture in this setting.
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Additional Information
Daqing Wan
Affiliation:
Department of Mathematics, University of California, Irvine, California 92697
MR Author ID:
195077
Email:
dwan@math.uci.edu
Keywords:
L-functions,
Fredholm determinants,
$p$-adic meromorphic continuation,
nuclear $\sigma$-modules,
Banach modules
Received by editor(s):
June 28, 1999
Received by editor(s) in revised form:
April 10, 2000
Published electronically:
June 6, 2000
Additional Notes:
This work was partially supported by the National Science Foundation
Article copyright:
© Copyright 2000
American Mathematical Society
