Unit roots of the unit root $L$-functions

Liping Yang; Hao Zhang

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arXiv · 2412.15667

Unit roots of the unit root $L$-functions

Liping Yang·Hao Zhang

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Abstract

Adolphson and Sperber characterized the unique unit root of $L$-function associated with toric exponential sums in terms of the $\mathcal{A}$-hypergeometric functions. For the unit root $L$-function associated with a family of toric exponential sums, Haessig and Sperber conjectured its unit root behaves similarly to the classical case studied by Adolphson and Sperber. Under the assumption of a lower deformation hypothesis, Haessig and Sperber proved this conjecture. In this paper, we demonstrate that Haessig and Sperber's conjecture holds in general.

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Liping Yang, Hao Zhang. 2024-12-20. Unit roots of the unit root $L$-functions. https://arxiv.org/abs/2412.15667

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