Counting rational points on transcendental curves in valued fields

2025/06/24 by Vermeulen, Floris
#FOS: Mathematics #Logic (math.LO) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2506.19411

Abstract

We prove upper bounds on the number of rational points on transcendental curves in arbitrary 1-h-minimal fields, similar to the Pila--Wilkie counting theorem in the o-minimal setting. These results extend results due to Cluckers--Comte--Loeser from p-adic fields to arbitrary valued fields of mixed characteristic. Our methods rely on parametrizations, where we avoid the usage of r-th power maps, combined with the determinant method.

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