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The mean value of the class numbers of cubic function fields

Author(s)
Lee, JungyunLee, YoonjinYoo, Jinjoo
Issued Date
2023-01
DOI
10.1016/j.jmaa.2022.126582
URI
https://scholarworks.unist.ac.kr/handle/201301/81408
Citation
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v.517, no.1, pp.126582
Abstract
We compute the mean value of |L(s,χ)|2 evaluated at s=1 when χ goes through the primitive cubic Dirichlet odd characters of A:=Fq[T], where Fq is a finite field with q elements and q≡1(mod3). Furthermore, we find the mean value of the class numbers for the cubic function fields Km=k(m3), where k:=Fq(T) is the rational function field, m∈A is a cube-free polynomial, and deg⁡(m)≡1(mod3). © 2022 Elsevier Inc.
Publisher
Academic Press Inc.
ISSN
0022-247X
Keyword (Author)
Cubic function fieldL-functionMean value of class numberMoment over function field

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