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The Density of Zeros of Dirichlet's L-Functions
Published online by Cambridge University Press: 20 November 2018
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Let L(s, χ) be a Dirichlet L-function and let N(σ, T, χ) denote the number of zeros ρ of L(s, χ), counted according to multiplicity, in the rectangle σ ≦ Re(ρ) ≦ 1, |Im(ρ)| ≦ T, (T ≦ 1). In this paper we shall prove several new estimates for the sum
where Σ* denotes summation over primitive characters only. These estimates will all be of the type
(1)
where denotes any fixed positive quantity.
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- Copyright © Canadian Mathematical Society 1979
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