Counting w-coprime S-integers and S-integral ideals in positive characteristic
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913991377289216 |
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| author | Liu, Si-Han Liu, Zhe-Cheng Yao, Jia-Yan |
| author_facet | Liu, Si-Han Liu, Zhe-Cheng Yao, Jia-Yan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10484 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Counting w-coprime S-integers and S-integral ideals in positive characteristic Liu, Si-Han Liu, Zhe-Cheng Yao, Jia-Yan Number Theory 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. |
| title | Counting w-coprime S-integers and S-integral ideals in positive characteristic |
| topic | Number Theory |
| url | https://arxiv.org/abs/2508.10484 |