Product formula of Artin symbols in non-abelian extensions
Volume 220 / 2025
Acta Arithmetica 220 (2025), 1-28
MSC: Primary 11R37; Secondary 11S31, 11R29, 11R27, 11R11, 05C22
DOI: 10.4064/aa240616-9-12
Published online: 30 June 2025
Abstract
The product formula for Artin symbols (norm residue symbols) connects local and global class field theory. Usually, the formula is considered in abelian extensions of global fields. In this paper, the product is considered in non-abelian extensions such that each symbol is well-defined. As an application, some properties of fundamental units of real quadratic fields are obtained.
