Displaying 41 – 60 of 172

Showing per page

Hilbert symbols, class groups and quaternion algebras

Ted Chinburg, Eduardo Friedman (2000)

Journal de théorie des nombres de Bordeaux

Let B be a quaternion algebra over a number field k . To a pair of Hilbert symbols { a , b } and { c , d } for B we associate an invariant ρ = ρ R [ 𝒟 ( a , b ) ] , [ 𝒟 ( c , d ) ] in a quotient of the narrow ideal class group of k . This invariant arises from the study of finite subgroups of maximal arithmetic kleinian groups. It measures the distance between orders 𝒟 ( a , b ) and 𝒟 ( c , d ) in B associated to { a , b } and { c , d } . If a = c , we compute ρ R ( [ 𝒟 ( a , b ) ] , [ 𝒟 ( c , d ) ] ) by means of arithmetic in the field k ( a ) . The problem of extending this algorithm to the general case leads to studying a finite graph associated...

Currently displaying 41 – 60 of 172