5 research outputs found
Letters from William Burnside to Robert Fricke: Automorphic Functions, and the Emergence of the Burnside Problem
Two letters from William Burnside have recently been found in the Nachlass of
Robert Fricke that contain instances of Burnside's Problem prior to its first
publication. We present these letters as a whole to the public for the first
time. We draw a picture of these two mathematicians and describe their
activities leading to their correspondence. We thus gain an insight into their
respective motivations, reactions, and attitudes, which may sharpen the current
understanding of professional and social interactions of the mathematical
community at the turn of the 20th century.Comment: documentclass amsart, 17 page
The decomposition of primes in torsion point fields
We investigate the decomposition of prime ideals in non-abelian extensions of number fields. These fields are generated by the coordinates of torsion points of elliptic curves without complex multiplications. We explain the necessary prerequisites from the theory of elliptic curves, modular forms, algebraic number theory, and invariant theory. Due to the complexity of the problem, complete results are restricted to torsion points of low order. These results are complemented by computational data which also cover some unsolved cases