M. Filaseta

activity

20042026

most citedFactorization of polynomials in hyperbolic geometry and dynamics

1 citations · 2 across the 16 of their papers we have counts for

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Showing 2023Show all

3 papers · 1 filter

math.NT2023

A generalization of a fourth irreducibility theorem of I. Schur

Martha Allen, Michael Filaseta

Let $u_{2 j}$ be the product of the odd positive integers $< 2 j$ . For $n$ an integer $\geq 1$ , define \[ f(x)=\sum_{j=0}^{n}a_j\frac{x^{2j}}{u_{2j+2}}, \] where the $a_{j}$ 's are arbit…

math.NT2023

On $n^{th}$ order Euler polynomials of degree $n$ that are Eisenstein

Michael Filaseta, Thomas Luckner

For $m$ an even positive integer and $p$ a prime, we show that the generalized Euler polynomial $E_{m p}^{(m p)} (x)$ is in Eisenstein form with respect to $p$ if and only if $p$ does…

math.NT2023

Generalized Sierpiński Numbers

Michael Filaseta, Robert Groth, Thomas Luckner

A Sierpiński number is a positive odd integer $k$ such that $k \cdot 2^{n} + 1$ is composite for all positive integers $n$ . Fix an integer $A$ with $2 \leq A$ . We show that there exis…

A generalization of a fourth irreducibility theorem of I. Schur

On nth order Euler polynomials of degree n that are Eisenstein

Generalized Sierpiński Numbers

On $n^{th}$ order Euler polynomials of degree $n$ that are Eisenstein