Spencer Hamblen

activity

20132024

most citedLocal arboreal representations

9 citations · 16 across the 7 of their papers we have counts for

collaborators

7 papers

math.NT2024

Waring Numbers of Ramified $p$ -adic Rings

Lucas Anthony, Joe Burton, Irene Deegbe +5

Let $p$ be prime and $e, k$ be positive integers, and let $R = Z_{p} [e p]$ . We calculate the Waring numbers $g_{R} (k)$ for many values of $p, e$ , and $k$ , and investig…

math.NT2022★ 1 cited

Roots of unity and higher ramification in iterated extensions

Spencer Hamblen, Rafe Jones

Given a field $K$ , a rational function $ϕ \in K (x)$ , and a point $b \in P^{1} (K)$ , we study the extension $K (ϕ^{- \infty} (b))$ generated by the union over $n$ of all solutions…

math.NT2020

Sums of Quaternion Squares and a Theorem of Watson

Tim Banks, Spencer Hamblen, Tim Sherwin +1

We use a representability theorem of G. L. Watson to examine sums of squares in Quaternion rings with integer coefficients. This allows us to determine a large family of such rings…

math.NT2019

Sums of Cubes in Quaternion Rings

Madison Gamble, Spencer Hamblen, Blake Schildhauer +1

We investigate a version of Waring's Problem over quaternion rings, focusing on cubes in quaternion rings with integer coefficients. We determine the global upper and lower bounds…

math.NT2016★ 2 cited

Sums of squares in Quaternion rings

Anna Cooke, Spencer Hamblen, Sam Whitfield

Lagrange's Four Squares Theorem states that any positive integer can be expressed as the sum of four integer squares. We investigate the analogous question over Quaternion rings, f…

math.NT2016★ 9 cited

Local arboreal representations

Jacqueline Anderson, Spencer Hamblen, Bjorn Poonen +1

Let $K$ be a field complete with respect to a discrete valuation $v$ of residue characteristic $p$ . Let $f (z) \in K [z]$ be a separable polynomial of the form $z^{ℓ} - c .$ Given $a \…

math.NT2013★ 4 cited

The density of primes in orbits of z^d + c

Spencer Hamblen, Rafe Jones, Kalyani Madhu

Given a polynomial f(z) = z^d + c over a global field K and a_0 in K, we study the density of prime ideals of K dividing at least one element of the orbit of a_0 under f. The densi…