Theorems of Hoheisel and of Ingham

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


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.


Absolute Constant Riemann Hypothesis Arithmetical Function Auxiliary Lemma Chapter Versus 
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Copyright information

© Springer-Verlag Berlin · Heidelberg 1970

Authors and Affiliations

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

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