The Method of I.M. Vinogradov in the Theory of the Zeta Function

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 VI in Basic Analytic Number Theory, 1993, pp 73-93 from Springer

Abstract: Abstract In this chapter we shall prove a mean value theorem due to I.M. Vinogradov, and from it deduce an estimate for the zeta function in a neighborhood of Re s = 1, a new boundary for zeros of the zeta function, and a new remainder term in the prime number theorem.

Date: 1993
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DOI: 10.1007/978-3-642-58018-5_6

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