On the index of the Stickelberger ideal and the cyclotomic regulator

Some asymptotic relations existing among arithmetical invariants of abelian fields are proved.     

An extended Stickelberger ideal of the compositum of a bicyclic field and an imaginary quadratic field

We consider certain extension of the Stickelberger ideal of the compositum of a bicyclic field and a quadratic imaginary field, obtained by adding new annihilators to the Stickelberger ideal. We compute the index of this extension, from which we get some divisibility properties for the relative class number of the compositum.     

On the stickelberger ideal of (2,...,2)-extensions of a cyclotomic number field

Let p be an odd prime number and n a natural number. Let K be a (2,...,2)-extension of the p^n−th cyclotomic number field obtained by adjoining ,..., , where m₁,...,m_t are rational integers. We get a system of generators of the minus part of the Stickelberger ideal of K, and calculate its index. This index is described as a product of some determinants of rational integer components. From this result, it is shown that the relative class number of K is expressed as this index.     

Enlargement of the group of circular units of a bicyclic field

We compute the index of a certain extension of Sinnott's group of circular units in the group of all units of a bicyclic field. From this index we obtain some divisibility properties for class numbers of bicyclic fields.     

Cyclotomic units and Stickelberger ideals of global function fields

In this paper, we define the group of cyclotomic units and Stickelberger ideals in any subfield of the cyclotomic function field. We also calculate the index of the group of cyclotomic units in the total unit group in some special cases and the index of Stickelberger ideals in the integral group ring.

     

Quasienergy basis for multielectron system in a strong laser field

The second-quantization procedure is performed in the basis of quasienergy states, and an expression is obtained for the Green's function of a finite Fermi system. A nonstationary effective potential is constructed in the Hartree-Fock and local-density approximations, and possibilities for using it are discussed.Voronezh Constructional Engineering Institute. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 97, No. 1, pp. 121–132, October, 1993.     

Normal basis for an ideal in a local ring

An effective construction is given for a normal ideal basis (when it exists) in local number field extensions with higher ramification.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 64, pp. 64–68, 1976.     

On the class number of p-th cyclotomic field

Let h^[-(p)h^-(p) be the relative class number of the p-th cyclotomic field. We show that logh^-(p) = [(p+3)/4] logp - [(p)/2] log2p+ log(1-b) + O(log₂² p)\log h^-(p) = {{p+3} \over {4}} \log p - {{p} \over {2}} \log 2\pi + \log (1-\beta ) + O(\log _2^2 p), where b\beta denotes a Siegel zero, if such a zero exists and p o -1 mod 4p\equiv -1\pmod {4}. Otherwise this term does not appear.