Footnote to the Titchmarsh-Linnik divisor problem

Abstract

The study of Ta(x) was initiated as long ago as 1931 by Titchmarsh [2]. Since the dispersion method is exceedingly complicated, it may be of interest to record that the theorem is a simple consequence of the recent result of Bombieri [3] on the average of the error term in the prime number theorem for arithmetic progressions. For our purpose the following, weaker, form of Bombieri's theorem is sufficient: (i) There exists a positive number B such that