On sums of sixteen squares (Q1092948)

Let \(r_{2s}(n)\) denote the number of representations of the natural number n by a sum of 2s squares. Then it is well-known that \(r_{2s}(n)\) can be expressed by sums of powers of divisors of n provided that \(s\leq 4\). In cases of \(s>4\) the formulas for \(r_{2s}(n)\) involve complicated arithmetical functions. The author now shows the interesting fact that \(r_{16}(n)\) can be represented only by divisor functions. His argument is based on well-known identities from the theory of elliptic modular functions.