Bounds of ideal class numbers of real quadratic function fields

2000/04/07 by Kunpeng Wang, Wang, Kunpeng, Xianke Zhang +1
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/0004190

arxiv created 2000/04/07 · openalex publication_date 2000/04/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The theory of continued fractions of functions √ D is used to give lower bound for class numbers h(D) of general real quadratic function fields K=k(√ D) over k=\bf F_q(T). For five series of real quadratic function fields K, the bounds of h(D) are given more explicitly, e.g., if D=F²+c, \hspace0.1cm then h(D)≥ degF /deg P; \hspace0.1cm if D=(SG)²+cS, then h(D)≥ degS / deg P; if D=(A^m+a)²+A, then h(D)≥ degA / deg P, where P is irreducible polynomial splitting in K, c∈ \bf F_q is any constant. In addition, six types of quadratic function fields are found to have ideal class numbers bounded and bigger than one. \bf keywords: quadratic function field, ideal class number, continued fractions of functions

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