Advertisement

Theorems of Hoheisel and of Ingham

  • K. Chandrasekharan
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 167)

Abstract

The prime number theorem implies that p n ~ nlogn, as n→∞, where p n denotes the nth prime. A related problem is to determine the size of the difference Pn + 1 - P n . The purpose of this chapter is to prove a theorem of Ingham’s which implies, in particular, that
$${p_{n + 1}} - {p_n} = 0\left( {p_n^{\frac{5} {8} + \varepsilon }} \right),\:as\quad n \to \infty$$
for every ε>0.

Keywords

Absolute Constant Riemann Hypothesis Arithmetical Function Auxiliary Lemma Chapter Versus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin · Heidelberg 1970

Authors and Affiliations

  • K. Chandrasekharan
    • 1
  1. 1.Eidgenössische Technische Hochschule ZürichDeutschland

Personalised recommendations