Rank one case of Dwork's conjecture
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Rank one case of Dwork's conjecture


In this paper, we prove the rank one case of Dwork’s conjecture on the p 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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