NUMBER THEORY IN FUNCTION FIELDS by Rosen, Michael ISBN 0387953353
From Student Book World
|
[edit] NUMBER THEORY IN FUNCTION FIELDS
Studies the relationship between number theory in algebraic number fields and algebraic function fields. This book explores various topics, including: the ABC-conjecture, Artin's conjecture on primitive roots, Drinfeld modules, the Brumer-Stark conjecture, and more. It is designed for graduates and professionals in mathematics and related fields.
This book studies the arithmetic of polynomial rings over finite fields, A=FT, and its relation to elementary number theory, which is concerned with the arithmetic properties of the ring of integers, Z, and its field of fractions, the rational numbers, Q. Early on in the development of elementary number theory, it was noticed that Z has many properties in common with A=FT, thereby leading one to suspect that many results which hold for Z have analogues of the ring A. The first few chapters of this book illustrate this by presenting, for example, analogues of the little theorems of Fermat and Euler, Wilson's theorem, quadratic (and higher) reciprocity, the prime number theorem, and Dirichlet's theorem on primes in an arithmetic progression. After presenting the needed foundational material about function fields, later chapters explore a variety of topics, including: the ABC-conjecture, Artin's conjecture on primitive roots, Drinfeld modules, the Brumer-Stark conjecture, class number formulae, and average value theorems. This book is designed for graduate students and professionals in mathematics and related fields who want to learn about the very fruitful relationship between number theory in algebraic number fields and algebraic function fields. In this book, many paths are set forth for future learning and exploration.
[edit] Book Details
[edit] Title
NUMBER THEORY IN FUNCTION FIELDS
[edit] Author
Rosen, Michael
[edit] ISBN
0387953353
[edit] Published
28/02/2002
[edit] Publisher
Springer-Verlag New York Inc.
[edit] Binding
hardback
[edit] Retail Price
42.5 (GBP)
[edit] Typical Price Online
38.25 (GBP)
[edit] Buy Book Online
If you wish to purchase NUMBER THEORY IN FUNCTION FIELDS, written by Rosen, Michael and published by Springer-Verlag New York Inc. on 28/02/2002 then we have listed a few select online book retailers who can provide good value and service.
| ISBN 0387953353 |
|---|
