Trevor Hyde

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20122026

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math.CO2018

Cyclotomic factors of necklace polynomials

Trevor Hyde

We observe that the necklace polynomials $M_{d} (x) = \frac{1}{d} \sum_{e ∣ d} μ (e) x^{d / e}$ are highly reducible over $Q$ with many cyclotomic factors. Furthermore, the seque…

math.NT2018

Normal elements in finite fields

Trevor Hyde

We give a simple derivation of the formula for the number of normal elements in an extension of finite fields. Our proof is based on the fact that units in the Galois group ring of…

math.NT2018

Liminal reciprocity and factorization statistics

Trevor Hyde

Let $M_{d, n} (q)$ denote the number of monic irreducible polynomials in $F_{q} [x_{1}, x_{2}, \dots, x_{n}]$ of degree $d$ . We show that for a fixed degree $d$ , the sequence $M_{d…