“…Our job now is to get a nontrivial estimate for (13), beyond square-root cancellation in the character sum S(m 1 , m 2 , n, h; q). For h = 0, the zero shift, the character sum S(m 1 , m 2 , n, 0; q) can be evaluated precisely, and then one can use the large sieve inequality of Duke, Friedlander and Iwaniec [8] for Kloosterman fractions to get extra cancellation on the sum over n and m. Alternatively one can use reciprocity and then Voronoi yet again on the sum over m 2 , to get a much better result. However for non-zero shift the character sum S(m 1 , m 2 , n, h; q) can not be computed explicitly, and hence it is not clear how to obtain extra cancellation.…”