CERTAIN IDENTITIES OF ZETA FUNCTIONS ON A QUATERNION ALGEBRA

Twisted Zeta Functions of Quaternion Orders

Given an abelian Galois extension K/F of number fields, a quaternion algebra A over F that is ramified at all infinite primes, and a character χ of the Galois group of K over F , we consider the twist of the zeta function of A by the character χ. We show that such twisted zeta functions provide a factorization of the zeta function of A(K) = A ⊗F K. Also, the quotient of the zeta function for A(...

A brief introduction to quaternion matrices and linear algebra and on bounded groups of quaternion matrices

The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...

Triple Integral Identities and Zeta Functions

Zeta-functions and Ideal Classes of Quaternion Orders

Inspired by Stark’s analytic proof of the finiteness of the class number of a ring of integers in an algebraic number field, we give a new proof of the finiteness of the number of classes of ideals in a maximal order of a quaternion division algebra over a totally real number field. Previous proofs of this well-known result have used adeles or geometry of numbers, while our proof uses the class...

Structure of Certain Banach Algebra Products

Let  and  be Banach algebras, ,  and . We define an -product on  which is a strongly splitting extension of  by . We show that these products form a large class of Banach algebras which contains all module extensions and triangular Banach algebras. Then we consider spectrum, Arens regularity, amenability and weak amenability of these products.