Todd Cochrane

collaborators

2 papers

math.NT2026

Mixed character sums modulo prime powers

Todd Cochrane, Andrew Granville

We obtain explicit estimates for the mixed character sum $S = S (I ¨ , g, f, p^{m}) = \sum_{x = 1}^{p^{m}} I ¨ (g (x)) e_{p^{m}} (f (x))$ , where $p^{m}$ is a prime power, $I ¨ $ is a multiplicative charac…

math.NT2026

Mixed incomplete character sums of rational functions with smooth moduli

Todd Cochrane, Andrew Granville, Junren Zheng

Let $I ¨ = I ¨ _{q}$ be a primitive character mod $q$ and fix $I^ > 0$ . In 1989 Graham and Ringrose gave strong bounds on character sums $\sum_{M < n \leq M + N} I ¨ (n)$ in intervals of length $N…