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arXiv · 2302.06328

Unit roots of the unit root $L$-functions of Kloosterman family

Liping Yang·Hao Zhang
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Abstract

As a consequence of Wan's theorem about Dwork's conjecture, the unit root $L$-functions of the $n$-dimensional Kloosterman family are $p$-adic meromorphic. By studying the symmetric power $L$-functions associated to the Kloosterman family, we prove that for each $0\le j\le n$, the unit root $L$-function coming from slope $j$ has a unique unit root which equals 1.

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Liping Yang, Hao Zhang. 2023-02-13. Unit roots of the unit root $L$-functions of Kloosterman family. https://arxiv.org/abs/2302.06328

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