Sums of almost equal prime squares
It is shown that almost all integers \(n\) satisfying the obvious congruence restrictions can be written as the sum of 3 resp. 4 squares of prime numbers \(p_i\), which have a distance not larger than \(n^{1/2-9/80+\varepsilon}\). The proof uses the circle method. The estimation of the minor arcs uses standard techniques. However, the treatment of the major arcs is more difficult. Although the computations begin as one would expect, approximating the exponential sum over primes by the exponential sum over all integers introduces several difficult error terms, and the main part of the paper is dedicated to the estimation of these terms.
scientific article; zbMATH DE number 5620968
scientific article