Rank one case of Dwork’s conjecture

Wan, Daqing

doi:10.1090/S0894-0347-00-00340-4

Rank one case of Dwork’s conjecture
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by Daqing Wan

J. Amer. Math. Soc. 13 (2000), 853-908

DOI: https://doi.org/10.1090/S0894-0347-00-00340-4

Published electronically: June 6, 2000

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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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Dwork’s conjecture on unit root zeta functions

150

Higher rank case of Dwork’s conjecture