Year: 2020
Type: preprint
Abstract: We show that assuming the generalized Riemann hypothesis there are no normal CM-fields with class number one of degree 64 and 96. This is done by constructing complete tables of normal CM-fields using discriminant bounds of Lee--Kwon. This solves the class number one problem for normal CM-fields assuming GRH. Using the same technique to solve the relative class number one problem in degrees 16, 32, 56 and 82, also the corresponding relative class number one problem is solved assuming GRH.
Source: arXiv (Cornell University)
Authors: Hofmann, Tommy, Sircana, Carlo
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3110567966