On the representations of a number as the sum of three squares

Abstract

if (h, k) 1. He remarked: When s = 2 or s>8, this conclusion is false. The cases s =3 and s =4 are exceptional. The conclusion is true, but new difficulties arise in the proof because the series used are not all absolutely convergent. These difficulties are easily surmounted when s =4, but are more serious when s = 3. It is the purpose of this paper to show that in spite of these convergence