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NON-VANISHING of L-FUNCTIONS for CYCLOTOMIC CHARACTERS in FUNCTION FIELDS
- Title
- NON-VANISHING of L-FUNCTIONS for CYCLOTOMIC CHARACTERS in FUNCTION FIELDS
- Authors
- Lee J.; Lee Y.
- Ewha Authors
- 이윤진
- SCOPUS Author ID
- 이윤진
- Issue Date
- 2022
- Journal Title
- Proceedings of the American Mathematical Society
- ISSN
- 0002-9939
- Citation
- Proceedings of the American Mathematical Society vol. 150, no. 2, pp. 455 - 468
- Keywords
- Central value; Cyclotomic character; Function field; L-function; Mean value
- Publisher
- American Mathematical Society
- Indexed
- SCIE; SCOPUS
- Document Type
- Article
- Abstract
- In the number field case, it is conjectured that the central values L(12 , χ) of L-functions are nonzero, where χ : (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(12 , ηχn) and that of L(12 , χn) for χn ∈ On, where f is a monic irreducible polynomial in A = Fq[t], Fq is the finite field of characteristic p, χn : (A/fnA)∗ → C∗ is a character with some p-power order, On is the set of all the primitive cyclotomic characters χn modulo fn with p-power order, g is a monic polynomial in A that is relatively prime to f, and η : (A/gA)∗ → C∗ is a primitive even character. 2021 American Mathematical Society
- DOI
- 10.1090/proc/15144
- Appears in Collections:
- 자연과학대학 > 수학전공 > Journal papers
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