Benjamin Klahn

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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

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

A Divisor problem for polynomials

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

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