scholarly journals Transfer of quadratic forms and of quaternion algebras over quadratic field extensions

2018 ◽  
Vol 111 (2) ◽  
pp. 135-143
Author(s):  
Karim Johannes Becher ◽  
Nicolas Grenier-Boley ◽  
Jean-Pierre Tignol
Keyword(s):  
Quadratic Forms ◽  
Quadratic Field ◽  
Quaternion Algebras ◽  
Field Extensions

27.—Generating Sets for Fuchsian Groups

1975 ◽  
Vol 72 (4) ◽  
pp. 317-326 ◽  
Author(s):  
J. H. H. Chalk ◽  
B. G. A. Kelly
Keyword(s):  
Quadratic Forms ◽  
Fundamental Region ◽  
Fuchsian Groups ◽  
Quaternion Algebras ◽  
Generating Sets ◽  
Complete Set ◽  
Explicit Bounds

SynopsisFor a class of Fuchsian groups, which includes integral automorphs of quadratic forms and unit groups of indefinite quaternion algebras, it is shown that the geometry of a suitably chosen fundamental region leads to explicit bounds for a complete set of generators.

scholarly journals Addendum: "Chain equivalences for symplectic bases, quadratic forms and tensor products of quaternion algebras"

2015 ◽  
Vol 14 (07) ◽  
pp. 1591001
Author(s):  
Adam Chapman
Keyword(s):  
Quadratic Forms ◽  
Tensor Products ◽  
Quaternion Algebras

We show how the chain lemma for quaternion algebras over fields of F ≠ 2 and [Formula: see text] can be strengthened so that up to two slots are changed at a time.

scholarly journals Central extensions and rational quadratic forms

1993 ◽  
Vol 130 ◽  
pp. 177-182 ◽  
Author(s):  
Yoshiomi Furuta ◽  
Tomio Kubota
Keyword(s):  
Central Extension ◽  
Quadratic Forms ◽  
Class Group ◽  
Quadratic Field ◽  
Abelian Extension ◽  
Narrow Sense ◽  
Maximal Extension ◽  
Central Extensions ◽  
Class Field ◽  
Ray Class Field

The purpose of this paper is to characterize by means of simple quadratic forms the set of rational primes that are decomposed completely in a non-abelian central extension which is abelian over a quadratic field. More precisely, let L = Q be a bicyclic biquadratic field, and let K = Q. Denote by the ray class field mod m of K in narrow sense for a large rational integer m. Let be the maximal abelian extension over Q contained in and be the maximal extension contained in such that Gal(/L) is contained in the center of Gal(/Q). Then we shall show in Theorem 2.1 that any rational prime p not dividing d1d2m is decomposed completely in /Q if and only if p is representable by rational integers x and y such that x ≡ 1 and y ≡ 0 mod m as followswhere a, b, c are rational integers such that b2 − 4ac is equal to the discriminant of K and (a) is a norm of a representative of the ray class group of K mod m.Moreover is decomposed completely in if and only if .

Sign in / Sign up

Export Citation Format

Share Document