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Dirichlet series satisfying a Riemann type functional equation and sharing one set.
- Source :
-
Complex Variables & Elliptic Equations . Oct2023, Vol. 68 Issue 10, p1653-1677. 25p. - Publication Year :
- 2023
-
Abstract
- In 2011, Li [A uniqueness theorem for Dirichlet series satisfying a Riemann type functional equation. Adv Math. 2011;226(5):4198–4211] proved that if two L-functions L 1 and L 2 satisfy the same functional equation with a (1) = 1 and L 1 − 1 (c j) = L 2 − 1 (c j) for two distinct finite complex numbers c 1 and c 2 , then L 1 = L 2. We prove that if two L-functions L 1 and L 2 have positive degree and satisfy the same functional equation with a (1) = 1 and E L 1 (S) = E L 2 (S) for a finite set S = { c 1 , c 2 , c 3 } , where c 1 , c 2 and c 3 are three distinct finite complex values, then L 1 = L 2. The main results of this paper are concerning some questions posed by Gross [Factorization of meromorphic functions and some open problems. Complex Analysis, Kentucky 1976 (Proc.Conf.); Berlin: Springer-Verlag; 1977. p. 51–69. (Lecture Notes in Mathematics; 599)]. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 17476933
- Volume :
- 68
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Complex Variables & Elliptic Equations
- Publication Type :
- Academic Journal
- Accession number :
- 171877406
- Full Text :
- https://doi.org/10.1080/17476933.2022.2069759