Sums of squares of |ζ(1 2 + it)| over short intervals are investigated. Known upper bounds for the fourth and twelfth moment of |ζ(1 2 + it)| are derived. A discussion concerning other possibilities for the estimation of higher power moments of |ζ(1 2 + it)| is given.

This is a translation of a paper [5] I wrote in 1971, and may help for Parimala’s course. Evidently completely outdated, but still may be useful. I changed some notation so as to be compatible with the course.

When a positive integer is expressed as a sum of squares, with each successive summand as large as possible, the summands decrease rapidly in size until the very end, where one may find two 4’s, or several 1’s. We find that the set of integers for which the summands are distinct does not have a natural density but that the counting function oscillates in a predictable way.