1. A. E. Ingham, On the difference between consecutive primes,Quart. J. of Math. Oxf. Ser.,8 (1937), pp. 255–266.
2. E. C. Titchmarsh,The theory of the Riemann zeta-functions, 2nd edition (Oxf., 1951), p. 81.
3. P. Turán,Eine neue Methode in der Analysis und deren Anwendungen, Akadémiai Kiadó (Budapest, 1953).
4. L. c.. II. Teil. Anwendungen, § 14, p. 158.
5. By performing the analysis more carefully the values 600 and 101/100 could have been replaced by much smaller resp. much greater values and also forc in (2. 2) a numerical value could have been obtained. According to an unpublished improvement I replaced (2. 1) by the estimation $$N(\alpha ,T)< c_6 T^{2(1 - \alpha ) + (1 - \alpha )^{1,14.} } .$$ .