Benjamin Klahn

most citedOn polynomials with roots modulo almost all primes

3 citations · 5 across the 5 of their papers we have counts for

collaborators

5 papers

math.NT2023

On sets of rational functions which locally represent all of $Q$

Benjamin Klahn, Joachim König

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…

math.NT2023

Galois groups of $(0 n) + (1 n) X + \dots + (6 n) X^{6}$

Benjamin Klahn, Marc Technau

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 o…

math.NT2022★ 2 cited

Large Subsets of $Z_{m}^{n}$ without Arithmetic Progressions

Christian Elsholtz, Benjamin Klahn, Gabriel F. Lipnik

For integers $m$ and $n$ , we study the problem of finding good lower bounds for the size of progression-free sets in $(Z_{m}^{n}, +)$ . Let $r_{k} (Z_{m}^{n})$ denot…

math.NT2022★ 3 cited

On polynomials with roots modulo almost all primes

Christian Elsholtz, Benjamin Klahn, Marc Technau

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…

math.NT2022

A Divisor problem for polynomials

Benjamin Klahn

We characterize all monic polynomials $f (x) \in Z [x]$ that have the property that \[f(p) \mid f(p^{p}),~\text{for all sufficiently large primes }p \geq N(f). \] We also gi…

On sets of rational functions which locally represent all of Q

Galois groups of (0n​)+(1n​)X+…+(6n​)X6

Large Subsets of Zmn​ without Arithmetic Progressions

On polynomials with roots modulo almost all primes

A Divisor problem for polynomials

On sets of rational functions which locally represent all of $Q$

Galois groups of $(0 n) + (1 n) X + \dots + (6 n) X^{6}$

Large Subsets of $Z_{m}^{n}$ without Arithmetic Progressions