Maillet determinants for real abelian number fields and its applications (Q2479815)

Let \(K\) be a real abelian number field. The purpose of the paper is to give a formula for the class number of \(K\) using a new definition of the Maillet determinant of \(K\). This definition is a modified version of the one given in [\textit{S. Kanemitsu} and \textit{T. Kuzumaki}, Acta Arith. 99, No. 4, 343--361 (2001; Zbl 0984.11056)], but it is convenient for applications. An example of an application is the following: suppose that \(K\) has conductor an odd prime number \(p\); a class number formula for intermediate fields of the cyclotomic \(\mathbb Z_p\)-extension of \(K\) is given in the form of a product of Maillet determinants.