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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
Published electronically: June 6, 2000
MathSciNet review: 1775761
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Abstract | References | Similar Articles | Additional Information


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

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