American Mathematical Society TranslationsSeries 2 1995; 267 pp; hardcover Volume: 166 ISBN10: 0821803875 ISBN13: 9780821803875 List Price: US$112 Member Price: US$89.60 Order Code: TRANS2/166
 Books in this series highlight some of the most interesting works presented at symposia sponsored by the St. Petersburg Mathematical Society. Aimed at researchers in number theory, field theory, and algebraic geometry, the present volume deals primarily with aspects of the theory of higher local fields and other types of complete discretely valuated fields. Most of the papers require background in local class field theory and algebraic \(K\)theory; however, two of them, "Unit Fractions" and "Collections of Multiple Sums", would be accessible to undergraduates. Readership Scientists working in number theory, field theory, or algebraic geometry. Table of Contents  A. I. Madunts and I. B. Zhukov  Multidimensional complete fields: Topology and other basic constructions
 V. A. Abrashkin  A ramification filtration of the Galois group of a local field
 B. M. Bekker  Class field theory for multidimensional complete fields with quasifinite residue fields
 D. G. Benois  On \(p\)adic representations arising from formal groups
 S. V. Vostokov  The pairing on \(K\)groups in fields of valuation of rank \(n\)
 S. V. Vostokov  ArtinHasse exponentials and Bernoulli numbers
 S. V. Vostokov and I. B. Zhukov  Some approaches to the construction of abelian extensions for \(\mathfrak p\)adic fields
 I. B. Zhukov  Structure theorems for complete fields
 O. Izhboldin and L. Kurliandchik  Unit fractions
 D. V. Fomin and O. T. Izhboldin  Collections of multiple sums
 A. I. Madunts  On convergence of series over local fields
 A. Nenashev  On Köck's conjecture about shuffle products
