Unit roots of the unit root $L$-functions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916535593861120 |
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| author | Yang, Liping Zhang, Hao |
| author_facet | Yang, Liping Zhang, Hao |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_15667 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unit roots of the unit root $L$-functions Yang, Liping Zhang, Hao Number Theory 11T23, 11S40 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. |
| title | Unit roots of the unit root $L$-functions |
| topic | Number Theory 11T23, 11S40 |
| url | https://arxiv.org/abs/2412.15667 |