Number theory in function fields / Michael Rosen.

Format:

Book

Author/Creator:

Rosen, Michael I. (Michael Ira), 1938-

Contributor:

Anne and Joseph Trachtman Memorial Book Fund.

Series:

Graduate texts in mathematics ; 210.

Graduate texts in mathematics ; 210

Language:

English

Subjects (All):

Number theory.

Finite fields (Algebra).

Physical Description:

xii, 358 pages : illustrations ; 25 cm.

Place of Publication:

New York : Springer, [2002]

Summary:

Elementary number theory is concerned with arithmetic properties of the ring of integers. 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, for example, analogues of the 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 required foundational material on function fields, the later chapters explore the analogy between global function fields and algebraic number fields. A variety of topics are presented, including: the ABiconjecture, Artin's conjecture on primitive roots, the Brumer-Stark conjecture, Drinfeld modules, class number formulae, and average value theorems.

Notes:

Includes bibliographical references (pages [341]-351) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Anne and Joseph Trachtman Memorial Book Fund.

ISBN:

0387953353

OCLC:

47238373