TY - JOUR

T1 - The mean value of the class numbers of cubic function fields

AU - Lee, Jungyun

AU - Lee, Yoonjin

AU - Yoo, Jinjoo

N1 - 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.

PY - 2023/1/1

Y1 - 2023/1/1

N2 - 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).

AB - 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).

KW - Cubic function field

KW - L-function

KW - Mean value of class number

KW - Moment over function field

UR - http://www.scopus.com/inward/record.url?scp=85136200878&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2022.126582

DO - 10.1016/j.jmaa.2022.126582

M3 - Article

AN - SCOPUS:85136200878

SN - 0022-247X

VL - 517

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

M1 - 126582

ER -