Twisted Zeta Functions of Quaternion Orders
نویسنده
چکیده
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(K) by the zeta function for A is entire when K/F is Galois of odd degree, not necessarily abelian.
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