Polynesian Journal of Mathematics

Volume 2, Issue 1

On the non-special divisors in algebraic function fields defined over finite fields

Stéphane Ballet and Mahdi Koutchoukali

Abstract:

In the theory of algebraic function fields and their applications to information theory, the Riemann–Roch theorem plays a fundamental role. But its use, delicate in general, is efficient and practical for applications especially in the case of non-special divisors. In this paper, we survey known results concerning non-special divisors in algebraic function fields defined over finite fields and enrich it with new results about the existence of such divisors in curves of defect $k$. Our presentation is self-contained with full proofs given for each result, either original proofs or shorter, alternative proofs.

Keywords: Finite field, function field, non-special divisor.

Citation:

Stéphane Ballet and Mahdi Koutchoukali. On the non-special divisors in algebraic function fields defined over finite fields. Polynesian Journal of Mathematics, Volume 2, Issue 1, Pages 1–41. (Mar. 2025) DOI: 10.69763/polyjmath.2.1

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Milestones:

Received 25 Oct 2024
Revised 22 Feb 2025
Accepted 3 Mar 2025
Published 7 Mar 2025
Communicated by Roger Oyono

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