Note on Tamagawa numbers of tori attached to CM algebras

Abstract

We prove that any integer power of $2$ can be realized as the Tamagawa number of a torus attached to a CM algebra considered by Guo Sheu Yu and Liang Yang Yu. Such a result is obtained by Liang Yang Yu under assuming "a generalized Landau conjecture". The main contribution of this paper is to remove the above assumption.