Prime Numbers in Arithmetic Progressions

Anatolij A. Karatsuba and Melvyn B. Nathanson
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Anatolij A. Karatsuba: Steklov Mathematical Institute
Melvyn B. Nathanson: School of Mathematics, Institute for Advanced Study

Chapter Chapter IX in Basic Analytic Number Theory, 1993, pp 122-140 from Springer

Abstract: Abstract The method of complex integration together with the results of L-functions proved in Chapter VIII will enable us to write down an explicit formula connecting the sum of values of the function Λ(n) over the integers lying in a given arithmetic progression with the zeros of an L-function. This explicit formula together with a theorem on the boundary of the zeros of the L-function will yield the prime number theorem for arithmetic progressions. We shall always assume below that k ≤ x.

Keywords: Asymptotic Formula; Dirichlet Series; Arithmetic Progression; Real Zero; Chapter VIII (search for similar items in EconPapers)
Date: 1993
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DOI: 10.1007/978-3-642-58018-5_9

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