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The mean value of the class numbers of cubic function fields
- Author(s)
- Lee, Jungyun, Lee, Yoonjin, Yoo, Jinjoo
- Issued Date
- 2023-01
- 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 field, L-function, Mean value of class number, Moment over function field
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