The mean value of the class numbers of cubic function fields

Jungyun Lee, Yoonjin Lee, Jinjoo Yoo

Research output: Contribution to journalArticlepeer-review


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).

Original languageEnglish
Article number126582
JournalJournal of Mathematical Analysis and Applications
Issue number1
StatePublished - 1 Jan 2023


  • Cubic function field
  • L-function
  • Mean value of class number
  • Moment over function field


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