A mean square asymptotic formula for sums of two k-th powers

Roger Baker, Brigham Young University
The number of representations of an integer as a sum of two relatively prime k-th powers (where k is at least 3) has summatory function T(x) approximately equal to a constant multiple of x^{2/k}. Let the remainder on subtracting this main term be E(x). We give an asymptotic formula for the mean square of E(x), subject to the existence of a suitable zero free strip for the Riemann zeta function. Unfortunately, no unconditional result of this kind is known.
The talk will be accessible to non-experts.