Kevin J. McGown

activity

20102026

most citedStatistics of genus numbers of cubic fields

2 citations · 5 across the 18 of their papers we have counts for

collaborators

Showing 2019Show all

4 papers · 1 filter

math.NT2019

The least primitive root modulo $p^{2}$

Bryce Kerr, Kevin McGown, Tim Trudgian

We provide an explicit estimate on the least primitive root mod $p^{2}$ . We show, in particular, that every prime $p$ has a primitive root mod $p^{2}$ that is less than $p^{0.99}$ .

math.NT2019

Explicit upper bounds on the least primitive root

Kevin J. McGown, Tim Trudgian

We give a method for producing explicit bounds on $g (p)$ , the least primitive root modulo $p$ . Using our method we show that $g (p) < 2 r 2^{r ω (p - 1)} p^{\frac{1}{4} + \frac{1}{4 r}}$ fo…

math.NT2019

Explicit bounds for small prime nonresidues

Shilin Ma, Kevin J. McGown, Devon Rhodes +1

Let $χ$ be a Dirichlet character modulo a prime~ $p$ . We give explicit upper bounds on $q_{1} < q_{2} < \dots < q_{n}$ , the $n$ smallest prime nonresidues of $χ$ . More precisely, given $n_{0}$ an…

math.NT2019

On the number of primes for which a polynomial is Eisenstein

Shilin Ma, Kevin McGown, Devon Rhodes +1

Previously Heyman and Shparlinski gave an asymptotic formula with error term for the number of Eisenstein polynomials of fixed degree and bounded height. Let $ψ (f)$ denote the numb…

The least primitive root modulo p2

Explicit upper bounds on the least primitive root

Explicit bounds for small prime nonresidues

On the number of primes for which a polynomial is Eisenstein

The least primitive root modulo $p^{2}$