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arXiv · 2508.10484

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

Si-Han Liu·Zhe-Cheng Liu·Jia-Yan Yao
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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.

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Si-Han Liu, Zhe-Cheng Liu, Jia-Yan Yao. 2025-08-14. Counting w-coprime S-integers and S-integral ideals in positive characteristic. https://arxiv.org/abs/2508.10484

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