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$p$-adic equidistribution and an application to $S$-units

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arxiv 2410.24088 v1 pith:373ZG2ZK submitted 2024-10-31 math.NT

Gerold Schefer This is my paper · ORCID
classification math.NT
keywords adicequidistributionapplicationmathbbrateresultclasscoefficients
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abstract

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 $\mathbb G_m^n$.

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  1. Heights of complete intersections in toric varieties

    math.AG 2024-12 accept novelty 5.0 of 10

    The height of intersections of two hypersurfaces twisted by torsion points on a toric variety converges to an adelic sum of mixed integrals of roof and Ronkin functions.

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