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The Density of Zeros of Dirichlet's L-Functions

Published online by Cambridge University Press:  20 November 2018

D. R. Heath-Brown
D. R. Heath-Brown*
Affiliation:
Trinity College, Cambridge, England
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 2 , 01 April 1979 , pp. 231 - 240
Copyright
Copyright © Canadian Mathematical Society 1979

References

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