Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character · 1924 · 65 citations · 0 references
Natural SciencesMathematicsGeometryNumber TheoryRepresentation TheoryAnalytic Number TheoryArithmetic GeometryIntegral SolutionsLattice Point Enumeration
Abstract 1. 1. We denote by r (n) the number of representations of n as the sum of two squares, representations which differ only in sign or order being counted as distinct; or, what is the same thing, the number of integral solutions of u2 + v2, (1. 11) or the coefficient of zn in the expansion (D (z) )2 = (1 + 2z + 2z4 + 2z9 + ...)2 = Ʃ∞0r (n)zn. (1. 12) If x is not an integer, or is negative, we write r (x) = 0.