J. Konig

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math.NT2025

Linear constellations in primes with arithmetic restrictions

Christopher Frei, Joachim KÃ¶nig, MagdalÃ©na TinkovÃ¡

We prove analogues of the theorem of Green and Tao on linear constellations in primes, in which the primes under consideration are restricted by certain arithmetic conditions. Our…

math.NT2025

A note on monogenic even polynomials

Joachim KÃ¶nig

We extend several predecessor works on even sextic monogenic polynomials. In particular, we prove a conjecture of Lenny Jones, thereby classifying even sextic monogenic polynomials…

math.NT2025

Critical Point Criteria and Dynamically Monogenic Polynomials

Joachim KÃ¶nig, Hanson Smith, Zack Wolske

Let $K$ be a number field with ring of integers $O_{K}$ , and let $f (x) \in O_{K} [x]$ be a monic, irreducible polynomial. We establish necessary and sufficient conditi…

math.NT2024

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

Benjamin Klahn, Joachim KÃ¶nig

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…

Linear constellations in primes with arithmetic restrictions

A note on monogenic even polynomials

Critical Point Criteria and Dynamically Monogenic Polynomials

On sets of rational functions which locally represent all of Q

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