The mean value of the class numbers of cubic function fields

Jungyun Lee, Yoonjin Lee, Jinjoo Yoo

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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).

Original languageEnglish
Article number126582
JournalJournal of Mathematical Analysis and Applications
Volume517
Issue number1
DOIs
StatePublished - 1 Jan 2023

Bibliographical note

Funding Information:
J. Lee is supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1I1A3057692 ). Y. Lee is supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. 2019R1A6A1A11051177 ) and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST)(NRF- 2022R1A2C1003203 ). J. Yoo is a corresponding author, and supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1A4A1016649 ) and Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. 2021R1I1A1A01047765 ).

Publisher Copyright:
© 2022 Elsevier Inc.

Keywords

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

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