컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0123 |
|---|---|
| 분류(Section) | Special Session |
| 분과(Session) | (SS-02) Some New and Young Results in Analytic Number Theory (SS-02) |
| 발표시간(Time) | 19th-B-13:30 -- 13:55 |
| 영문제목 (Title(Eng.)) |
Average value of the divisor class numbers of real cubic function fields |
| 저자(Author(s)) |
Jungyun Lee1, Yoonjin Lee2, Jinjoo Yoo3 Kangwon National University1, Ewha Womans University2, UNIST3 |
| 초록본문(Abstract) | We compute an asymptotic formula for the divisor class numbers of \textit{real} cubic function fields $K_m = k(\sqrt[3]{m})$, where $\mathbb{F}_q$ is a finite field with $q$ elements, $q \equiv 1 \pmod 3$, $k:=\mathbb{F}_q(T)$ is the rational function field, and $m \in \mathbb{F}_q[T]$ 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 $|L(s,\chi)|^2$ evaluated at $s=1$ when $\chi$ goes through the primitive cubic \textit{even} Dirichlet characters of $\mathbb{F}_q[T]$, where $L(s,\chi)$ is the associated Dirichlet $L$-function. This is joint work with Jungyun Lee and Yoonjin Lee. |
| 분류기호 (MSC number(s)) |
11M38, 11R29 |
| 키워드(Keyword(s)) | Average value of class number, cubic function field |
| 강연 형태 (Language of Session (Talk)) |
Korean |