During his PhD studies, Mathias Løkkegaard Laursen studied criteria for irrationality, transcendence, or linear independence of numbers expressed as infinite series, as infinite products, as infinite products, or as infinite continued fractions. The respective numbers are in all cases generated by sequences of algebraic numbers where the absolute values satisfy a certain growth condition. This study led to generalizations, and in some cases improvements, of several such criteria as well as new criteria for algebraic independence of numbers expressed as infinite series of rational numbers.

In parallel to the main studies above, Mathias Løkkegaard Laursen also determined the attainable p-adic measure values within two families of sets of p-adic numbers inspired by the family of sets described by the Duffin–Schaeffer Conjecture. Finally, Mathias Løkkegaard Laursen was also part of a study that determined the analytical equivalence of the partition function associated with the Fibonacci numbers.

The PhD study was completed at the Department of Mathematics, Faculty of Natural Sciences, Aarhus University.

This summary was prepared by the PhD student.

Time: Friday, 20 June 2025 at 14:00
Place: Building 1532, room 116, Lecture Theatre G1 Department of Mathematics, Aarhus University, Ny Munkegade 118, 8000 Aarhus C
Title of PhD thesis: Irrationality, transcendence, and other subjects in number theory
Contact information: Mathias Løkkegaard Laursen, e-mail: mll@math.au.dk, tel.: +45 42797086
Members of the assessment committee:
Professor Florian Luca, Department of Mathematical Sciences, Stellenbosch University, South Africa
Professor Wadim Zudilin, Mathematics, Radboud University, Netherlands 
Professor Peter Jørgensen (chair), Department of Mathematics, Aarhus University, Denmark
Main supervisor: Professor Simon Kristensen, Department of Mathematics, Aarhus University, Denmark
Language: The PhD dissertation will be defended in English

The defence is public.
The PhD thesis is available for reading at the Graduate School of Natural Sciences/GSNS, Ny Munkegade 120, building 1521, 8000 Aarhus C