S. Glasby

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20242026

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math.NT2026

Hilbert's Theorem 90, periodicity, and roots of Artin-Schreier polynomials

S. P. Glasby

Let $E / F$ be a cyclic field extension of degree $n$ , and let $I ¨ $ generate the group $Gal (E / F)$ . If $Tr_{F}^{E} (y) = \sum_{i = 0}^{n - 1} I ¨ ^{i} y = 0$ , then the additive form of Hilb…

math.NT2024

Maximizing weighted sums of binomial coefficients using generalized continued fractions

S. P. Glasby, G. R. Paseman

Let $m, r \in Z$ and $I ¨ \in R$ satisfy $0 ⩽ r ⩽ m$ and $I ¨ ⩾ 1$ . Our main result is a generalized continued fraction for an expression involving t…