Karsten Muller

collaborators

3 papers

math.NT2026

The Bombieri--van der Poorten Formula for Partial Quotients of Higher Degree Algebraic Irrationals

Karsten MÃ¼ller

The fundamental relationship between the partial quotients $b_{n + 1}$ of an algebraic irrational $I^\pm = m k$ and its corresponding algebraic form $d_{n} = ∣ p_{n}^{m} - k q_{n}^{m} ∣$ was…

math.NT2026

Gain Bounds for Diagonal Superelliptic Equations under the Strong ABC Conjecture

Karsten MÃ¼ller

We establish a novel framework for bounding the adapted power gain $G_{p}$ and approximation gain $G_{a}$ of coprime integer solutions to the generalized diagonal superelliptic equatio…

math.NT2026

From ABC to Effective Roth and Ridout Constants for Cubic Roots

Karsten MÃ¼ller, Michael Taktikos

Enrico Bombieri showed conditionally (1994) that the ABC conjecture implies Roth's theorem, and Van Frankenhuysen (1999) later provided a complete proof. Building on Bombieri's and…