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 ...

Using the group consisting of the eight Möbius transformations x, –x, 1/x, –1/x, (x – 1)/(x + 1), (x + 1)/(1 – x), (x + 1)/(x – 1), and (1 – x)/(x + 1), we present an enumerative proof of the ...