Todd Cochrane

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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…

math.NT2018

A generalization of the Goresky-Klapper conjecture, Part II

Todd Cochrane, Michael J. Mossinghoff, Chris Pinner +1

Suppose that $f (x) = A x^{k}$ mod $p$ is a permutation of the least residues mod $p$ . With the exception of the maps $f (x) = A x$ and $A x^{(p + 1) /2}$ mod $p$ we show that for fixed $n\geq 2…

math.NT2018

A generalization of the Goresky-Klapper conjecture, Part I

Badria Alsulmi, Todd Cochrane, Michael J. Mossinghoff +4

For a fixed integer $n \geq 2,$ we show that a permutation of the least residues mod $p$ of the form $f (x) = A x^{k}$ mod $p$ cannot map a residue class mod $n$ to just one residue class…