Todd Cochrane

activity

20142026

collaborators

Showing 2026Show all

2 papers · 1 filter

math.NT2026

Mixed character sums modulo prime powers

Todd Cochrane, Andrew Granville

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

math.NT2026

Mixed incomplete character sums of rational functions with smooth moduli

Todd Cochrane, Andrew Granville, Junren Zheng

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