A study of Inkeriʹs class number formula

Let p be an odd prime and be the cyclotomic field defined by a primitive pth root of unity ζp. It is well-known that the relative class number of can be expressed by means of the determinant of Inkeriʹs matrix. The main purpose of this paper is to study Inkeriʹs class number formula from the viewpoints of bases of Stickelberger ideals in a certain group ring and some special polynomial values.