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 -