Abstract
Abstract In this paper, by using the idea of truncated counting functions, we study the uniqueness of transcendental meromorphic functions and L-functions whose certain nonlinear differential polynomials share one finite nonzero value. The result in this paper extends the theorem given by Liu, Li and Yi.
Highlights
L-functions in the Selberg class, with the Riemann zeta function as a prototype, are important objects in number theory, and value distribution of L-functions has been studied extensively
In this paper, by using the idea of truncated counting functions, we study the uniqueness of transcendental meromorphic functions and L-functions whose certain nonlinear di erential polynomials share one nite nonzero value
(iii) Functional equation: L satis es a functional equation of type
Summary
L-functions in the Selberg class, with the Riemann zeta function as a prototype, are important objects in number theory, and value distribution of L-functions has been studied extensively. Throughout the paper, an L-function always means an L-function L in the Selberg class, which includes the Riemann zeta function ζ (s) =. N−s and essentially those Dirichelet series where one might expect a Riemann hypothesis. Such an L-function is de ned to be a Dirichelet series L(s) =. With positive real numbers Q, λj, and complex numbers νj, ω with Reνj ≥ and |ω| =. Unless n is a positive power of a prime and b(n) nθ for some θ
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