NON-VANISHING OF L-FUNCTIONS FOR CYCLOTOMIC CHARACTERS IN FUNCTION FIELDS
- 주제(키워드) Function field , L-function , central value , mean value , cyclotomic character
- 주제(기타) Mathematics, Applied
- 주제(기타) Mathematics
- 설명문(일반) [Lee, Jungyun] Kangwon Natl Univ, Dept Math Educ, Chuncheon Si 24341, Gangwon Do, South Korea; [Lee, Yoonjin] Ewha Womans Univ, Dept Math, 52 Ewhayeodae Gil, Seoul 03760, South Korea
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- OA유형 hybrid
- 발행기관 AMER MATHEMATICAL SOC
- 발행년도 2022
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000190360
- 본문언어 영어
- Published As https://doi.org/10.1090/proc/15144
초록/요약
In the number field case, it is conjectured that the central values L(1/2, chi) of L-functions are nonzero, where chi : (Z/mZ)* -> C* is a primitive Dirichlet character with conductor m. We resolve this conjecture in the function field case by proving that there are infinitely many cyclotomic characters for which the central values of L-functions are nonzero. In detail, for a given positive integer n, we compute the mean value of L(1/2, eta chi(n)) and that of L(1/2, chi(n)) for chi(n) is an element of O-n, where f is a monic irreducible polynomial in A = F-q[t], F-q is the finite field of characteristic p, chi(n) : (A/f(n) A)* -> C* is a character with some p-power order, O-n is the set of all the primitive cyclotomic characters chi(n) modulo f(n) with p-power order, g is a monic polynomial in A that is relatively prime to f, and eta : (A/gA)* -> C* is a primitive even character.
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