$p$-adic equidistribution and an application to $S$-units
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912098475311104 |
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| author | Schefer, Gerold |
| author_facet | Schefer, Gerold |
| contents | We prove a Galois equidistribution result for torsion points in $\mathbb G_m^n$ in the $p$-adic setting for test functions of the form $\log |F|_p$ where $F$ is a nonzero polynomial with coefficients in the $p$-adic numbers. Our result includes a power saving quantitative estimate of the decay rate rate of the equidistribution. As an application we show that Ih's Conjecture is true for a class of divisors of $\mathbb G_m^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_24088 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $p$-adic equidistribution and an application to $S$-units Schefer, Gerold Number Theory 11J61 (Primary) 11R06 (Secondary) We prove a Galois equidistribution result for torsion points in $\mathbb G_m^n$ in the $p$-adic setting for test functions of the form $\log |F|_p$ where $F$ is a nonzero polynomial with coefficients in the $p$-adic numbers. Our result includes a power saving quantitative estimate of the decay rate rate of the equidistribution. As an application we show that Ih's Conjecture is true for a class of divisors of $\mathbb G_m^n$. |
| title | $p$-adic equidistribution and an application to $S$-units |
| topic | Number Theory 11J61 (Primary) 11R06 (Secondary) |
| url | https://arxiv.org/abs/2410.24088 |