Maillet's determinant and a certain basis of the Stickelberger ideal

Rok, strany: 1997, 121 - 128

In the first section we transform Maillet's determinant $D_q$, where $q$ is a power of an odd prime, into a new matrix $M_q$, whose determinant is equal to $\pm h^-_q$, as follows from a determinant formula proved by Metsänkylä (1967) [T. Metsänkylä: Bemerkungen über den ersten Faktor der Klassenzahl des Kreisk&ooml;rpers, Annales Universitatis Turkuensis 105 (1967), 1–15]. The value of $D_q$ is hence obtained. In the second section we prove that the above matrix $M_q$ is a transition matrix to a certain $Z$-basis of the Stickelberger ideal of the $q$-th cyclotomic field (giving thus another proof of Iwasawa's class number formula). We obtain new $Z$-bases of the Stickelberger ideal. The approach and methods are based on and generalize the results of Jha (1993), who considered only the case when $q$ is an odd prime.

ISO 690:

Fuchs, P. 1997. Maillet's determinant and a certain basis of the Stickelberger ideal. In Tatra Mountains Mathematical Publications, vol. 11, no.2, pp. 121-128. 1210-3195.

APA:

Fuchs, P. (1997). Maillet's determinant and a certain basis of the Stickelberger ideal. Tatra Mountains Mathematical Publications, 11(2), 121-128. 1210-3195.