On the representation of a number as the sum of any number of squares, and in particular of five

Abstract

1. 1. In a short note published recently in the P r o c e e d i n g s o f t h.e National Academy of Sciences' I sketched the outlines of a. new solution of one of the most interesting and difficult problems in the Theory of Numbers, that of determining the number of representations of a given integer as the sum of five or seven squares. The method which I use is one of great power and generality, and has been applied by Mr. J. E. Littlewood, Mr. S. Ramanujan, and myself to the solution of a number of different problems; and it is probable that, in our previous writings on the subject,2 we have explained sufficiently the general ideas on which it rests. I may therefore confine myself, for the most part, to filling in the details of my previous work. I should observe, however, that the method by which I now sum the singular series , which plays a dominant role in the analysis,

Locations

• Transactions of the American Mathematical Society - View - PDF