A study of Inkeri's class number formula

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