4 papers
Monogenity of the irreducible factors of -Fibonacci and -Lucas polynomials
Michail Karatarakis, Sumandeep Kaur
In this article, we study the monogenity of the number field generated by a root of an irreducible factor of the generalized -Fibonacci and -Lucas polynomial sequence…
A Local Approach to Monogenity with an Application to Lenny Jones' Conjecture
Michail Karatarakis, Sumandeep Kaur
The study of monogenic polynomials is a classical problem in algebraic number theory. Existing criteria for deciding whether a polynomial is monogenic typically rely on discriminan…
A formalization of the Gelfond-Schneider theorem
Michail Karatarakis, Freek Wiedijk
We formalize Hilbert's Seventh Problem and its solution, the Gelfond-Schneider theorem, in the Lean 4 proof assistant. The theorem states that if and are algebraic numbers…
Formalized Hopfield Networks and Boltzmann Machines
Matteo Cipollina, Michail Karatarakis, Freek Wiedijk
Neural networks are widely used, yet their analysis and verification remain challenging. We present a Lean~4 formalization covering both deterministic and stochastic models. We fir…