In this paper we bound character sums of the shape ∑ n≤N χ 1 f n χ 2 f n+l , ; where χ1 and χ2 are non-principal multiplicative characters modulo a prime p, f(x) is a real-valued, twice-differentiable ...

Consecutive numbers are ones that follow on from each other in order, like 2, 3, 4 and 5. We can create certain numbers by adding together runs of consecutive numbers, e.g. 1 + 2 + 3 = 6 or 14 + 15 = ...