**American Mathematical Society Translations - Series 2**

1995;
267 pp;
Hardcover

MSC: Primary 11;

**Print ISBN: 978-0-8218-0387-5
Product Code: TRANS2/166**

List Price: $126.00

AMS Member Price: $100.80

MAA Member Price: $113.40

**Electronic ISBN: 978-1-4704-3377-2
Product Code: TRANS2/166.E**

List Price: $118.00

AMS Member Price: $94.40

MAA Member Price: $106.20

# Proceedings of the St. Petersburg Mathematical Society Volume III

Share this page *Edited by *
*O. A. Ladyzhenskaya*

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

## Proceedings of the St. Petersburg Mathematical Society Volume III

- Cover Cover11
- Title page v6
- Copyright page vi7
- Dedication vii8
- Contents ix10
- Multidimensional complete fields: Topology and other basic constructions 112
- A ramification filtration of the Galois group of a local field 3546
- Class field theory for multidimensional complete fields with quasifinite residue fields 101112
- On 𝑝-adic representations arising from formal groups 107118
- The pairing on 𝐾-groups in fields of valuation of rank 𝑛 111122
- Artin-Hasse exponentials and Bernoulli numbers 149160
- Some approaches to the construction of abelian extensions for 𝔭-adic fields 157168
- Structure theorems for complete fields 175186
- Unit fractions 193204
- Collections of multiple sums 201212
- On convergence of series over local fields 215226
- On Köck’s conjecture about shuffle products 235246
- Back Cover Back Cover1281