| Abstrakt: |
In the present paper, we prove that the generalized Riemann hypothesis for the Dirichlet L-function L (s , χ) is equivalent to the following bound: Let k ≥ 1 and ℓ be positive real numbers. For any ϵ > 0 , we have ∑ n = 1 ∞ χ (n) μ (n) n k exp - x n ℓ = O ϵ , k , ℓ (x - k ℓ + 1 2 ℓ + ϵ ) , as x → ∞ , where χ is a primitive Dirichlet character modulo q, and μ (n) denotes the Möbius function. This bound generalizes the previous bounds given by Riesz, and Hardy–Littlewood. [ABSTRACT FROM AUTHOR] |
Full text from SpringerLink