Counting w-coprime S-integers and S-integral ideals in positive characteristic

2025/08/14 by Liu, Si-Han, Liu, Zhe-Cheng, Yao, Jia-Yan
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.10484

Abstract

Let Fq be the finite field with q elements, and K an algebraic function field over with Fq as its field of constants. Let S be a finite nonempty set of prime divisors over K, and OS be the ring of integers of K attached to S. Let w greater than 1 be an integer. In this work we shall count w coprime S integers and S integral ideals, and our proofs are a combination of analytic methods and the Riemann Roch theorem and the Weil theorem for function fields in positive characteristic.

Citations

• The Density of Tuples Restricted by Relatively r-Prime Conditions
• Tuples of polynomials over finite fields with pairwise coprimality\n conditions
• The distribution of lattice points with relatively r-prime
• Uniform Probability and Natural Density of Mutually Left Coprime\n Polynomial Matrices over Finite Fields

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