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Average value of the divisor class numbers of real cubic function fields

Author(s)
Lee, YoonjinLee, JungyunYoo, Jinjoo
Issued Date
2023-01
DOI
10.1515/math-2023-0160
URI
https://scholarworks.unist.ac.kr/handle/201301/81311
Citation
OPEN MATHEMATICS, v.21, no.1, pp.20230160
Abstract
We compute an asymptotic formula for the divisor class numbers of real cubic function fields K = k( m) m 3, where q is a finite field with q elements, q = 1 (mod 3), k. (T) q is the rational function field, and m. [T] q is a cube-free polynomial; in this case, the degree of m is divisible by 3. For computation of our asymptotic formula, we find the average value of |L(s,.)|2 evaluated at s = 1 when. goes through the primitive cubic even Dirichlet characters of [T] q, where L(s,.) is the associated Dirichlet L-function.
Publisher
DE GRUYTER POLAND SP Z O O
ISSN
2391-5455
Keyword (Author)
L-functionaverage value of class numbercubic function fieldmoment over function field
Keyword
L-SERIES

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