David Krumm

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20172020

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math.NT2018

Twists of hyperelliptic curves by integers in progressions modulo $p$

David Krumm, Paul Pollack

Let $f (x)$ be a nonconstant polynomial with integer coefficients and nonzero discriminant. We study the distribution modulo primes of the set of squarefree integers $d$ such that t…

math.NT2018

A finiteness theorem for specializations of dynatomic polynomials

David Krumm

Let $t$ and $x$ be indeterminates, let $ϕ (x) = x^{2} + t \in Q (t) [x]$ , and for every positive integer $n$ let $Φ_{n} (t, x)$ denote the $n^{th}$ dynatomic polynomial of $ϕ$ . Let…

math.NT2017

Galois groups in a family of dynatomic polynomials

David Krumm

For every nonconstant polynomial $f \in Q [x]$ , let $Φ_{4, f}$ denote the fourth dynatomic polynomial of $f$ . We determine here the structure of the Galois group and the degree…

Twists of hyperelliptic curves by integers in progressions modulo p

A finiteness theorem for specializations of dynatomic polynomials

Galois groups in a family of dynatomic polynomials

Twists of hyperelliptic curves by integers in progressions modulo $p$