Number Theory in Function Fields
Number Theory in Function Fields

Author: Michael Rosen

Publisher: Springer Science & Business Media

Published: 2013-04-18

Total Pages: 355

ISBN-13: 1475760469

DOWNLOAD EBOOK

Early in the development of number theory, it was noticed that the ring of integers has many properties in common with the ring of polynomials over a finite field. The first part of this book illustrates this relationship by presenting analogues of various theorems. The later chapters probe the analogy between global function fields and algebraic number fields. Topics include the ABC-conjecture, Brumer-Stark conjecture, and Drinfeld modules.

Singularity Theory and Some Problems of Functional Analysis
Singularity Theory and Some Problems of Functional Analysis

Author: Semen Grigorʹevich Gindikin

Publisher: American Mathematical Soc.

Published: 1992

Total Pages: 212

ISBN-13: 9780821875025

DOWNLOAD EBOOK

The emergence of singularity theory marks the return of mathematics to the study of the simplest analytical objects: functions, graphs, curves, surfaces. The modern singularity theory for smooth mappings, which is currently undergoing intensive developments, can be thought of as a crossroad where the most abstract topics (such as algebraic and differential geometry and topology, complex analysis, invariant theory, and Lie group theory) meet the most applied topics (such as dynamical systems, mathematical physics, geometrical optics, mathematical economics, and control theory). The papers in this volume include reviews of established areas as well as presentations of recent results in singularity theory. The authors have paid special attention to examples and discussion of results rather than burying the ideas in formalism, notation, and technical details. The aim is to introduce all mathematicians - as well as physicists, engineers, and other consumers of singularity theory - to the world of ideas and methods in this burgeoning area.