T. E. O. Silva

activity

20152019

collaborators

3 papers

math.NT2019

The distribution of $k$ -free numbers

Michael J. Mossinghoff, Tomás Oliveira e Silva, Tim Trudgian

Let $R_{k} (x)$ denote the error incurred by approximating the number of $k$ -free integers less than $x$ by $x / ζ (k)$ . It is well known that $R_{k} (x) = Ω (x^{\frac{1}{2 k}})$ , and widely co…

math.NT2017

Linear combinations of primitive elements of a finite field

Stephen Cohen, Tomás Oliveira e Silva, Nicole Sutherland +1

We examine linear sums of primitive roots and their inverses in finite fields. In particular, we refine a result by Li and Han, and show that every $p > 13$ has a pair of primitive…

math.NT2015

On Grosswald's conjecture on primitive roots

Stephen D. Cohen, Tomás Oliveira e Silva, Tim Trudgian

Grosswald's conjecture is that $g (p)$ , the least primitive root modulo $p$ , satisfies $g (p) \leq p - 2$ for all $p > 409$ . We make progress towards this conjecture by proving…

The distribution of k-free numbers

Linear combinations of primitive elements of a finite field

On Grosswald's conjecture on primitive roots

The distribution of $k$ -free numbers