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math.NT2025
Computing class groups and unit groups in Magma
Andreas-Stephan Elsenhans, John Voight
We describe the computation of class groups and unit groups of number fields as implemented in Magma (V2.29). After quickly reviewing the main algorithms based on factor bases, rel…
math.NT2025
Numerical verification of the Collatz conjecture for billion digit random numbers
Andreas-Stephan Elsenhans
The Collatz conjecture, also known as the 3n+1 problem, is one of the most popular open problems in number theory. In this note, an algorithm for the verification of the Collatz co…
math.NT2025
Explicit modularity of K3 surfaces with complex multiplication of large degree
Edgar Costa, Andreas-Stephan Elsenhans, Jörg Jahnel +1
We consider the transcendental motive of three K3 surfaces conjectured to have complex multiplication (CM). Under this assumption, we match these to explicit algebraic Hecke qu…