Výsledky vyhledávání - "Klahn, Benjamin"

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On sets of rational functions which locally represent all of $\mathbb{Q}$

Publikováno v: J. Algebra 653 (2024), 1--24

We investigate finite sets of rational functions $\{ f_{1},f_{2}, \dots, f_{r} \}$ defined over some number field $K$ satisfying that any $t_{0} \in K$ is a $K_{p}$-value of one of the functions $f_{i}$ for almost all primes $p$ of $K$. We give stron

Externí odkaz: http://arxiv.org/abs/2306.12630

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Galois groups of $\binom{n}{0} + \binom{n}{1} X + \ldots + \binom{n}{6} X^6$

Autor: Klahn, Benjamin, Technau, Marc

We show that the Galois group of the polynomial in the title is isomorphic to the full symmetric group on six symbols for all but finitely many $n$. This complements earlier work of Filaseta and Moy, who studied Galois groups of $\binom{n}{0} + \bino

Externí odkaz: http://arxiv.org/abs/2304.12658

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Large Subsets of $\mathbb{Z}_m^n$ without Arithmetic Progressions

Autor: Elsholtz, Christian, Klahn, Benjamin, Lipnik, Gabriel F.

For integers $m$ and $n$, we study the problem of finding good lower bounds for the size of progression-free sets in $(\mathbb{Z}_{m}^{n},+)$. Let $r_{k}(\mathbb{Z}_{m}^{n})$ denote the maximal size of a subset of $\mathbb{Z}_{m}^{n}$ without arithme

Externí odkaz: http://arxiv.org/abs/2211.02588

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On polynomials with roots modulo almost all primes

Autor: Elsholtz, Christian, Klahn, Benjamin, Technau, Marc

Publikováno v: Acta Arith. 205:3, 251--263 (2022)

Call a monic integer polynomial exceptional if it has a root modulo all but a finite number of primes, but does not have an integer root. We classify all irreducible monic integer polynomials $h$ for which there is an irreducible monic quadratic $g$

Externí odkaz: http://arxiv.org/abs/2206.13466

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A Divisor problem for polynomials

Autor: Klahn, Benjamin

We characterize all monic polynomials $f(x) \in \mathbb{Z}[x]$ that have the property that \[f(p) \mid f(p^{p}),~\text{for all sufficiently large primes }p \geq N(f). \] We also give necessary conditions and a sufficient condition for monic polynomia

Externí odkaz: http://arxiv.org/abs/2202.02100

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