Counting w-coprime S-integers and S-integral ideals in positive characteristic
Number Theory
2025-08-15 v1
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.
Cite
@article{arxiv.2508.10484,
title = {Counting w-coprime S-integers and S-integral ideals in positive characteristic},
author = {Si-Han Liu and Zhe-Cheng Liu and Jia-Yan Yao},
journal= {arXiv preprint arXiv:2508.10484},
year = {2025}
}