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Field arithmetic by Michael D. Fried

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Published by Springer in Berlin .
Written in English

Subjects:

  • Algebraic fields,
  • Algebraic number theory

Book details:

Edition Notes

Includes bibliographical references (p. [761]-779) and index.

StatementMichael D. Fried, Moshe Jarden.
SeriesErgebnisse der Mathematik und ihrer Grenzgebiete -- 3. Folge, v. 11 = -- A series of modern surveys in mathematics, Ergebnisse der Mathematik und ihrer Grenzgebiete -- 3. Folge, Bd. 11.
ContributionsJarden, Moshe, 1942-
Classifications
LC ClassificationsQA247 .F73 2008
The Physical Object
Paginationxxiii, 792 p. :
Number of Pages792
ID Numbers
Open LibraryOL17020934M
ISBN 103540772693
ISBN 109783540772699
LC Control Number2008924174

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Field Arithmetic. Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments.   System Upgrade on Tue, May 19th, at 2am (ET) During this period, E-commerce and registration of new users may not be available for up to 12 hours. Finite Field Arithmetic The efficient implementation of finite field arithmetic is an important prerequisite in elliptic curve systems because curve operations are performed using arithmetic op- erations in the underlying field. § provides an informal introduction to the theory.   A major, and relatively recent, topic in the arithmetic of fields has been the gradual introduction of the language and techniques of mathematical logic: ultraproducts, model theory, non-standard structures, decision problems and effective methods.

Product Information. This book provides an exposition of function field arithmetic with emphasis on recent developments concerning Drinfeld modules, the arithmetic of special values of transcendental functions (such as zeta and gamma functions and their interpolations), diophantine approximation and related interesting open problems. Field Arithmetic by Michael D. Fried, , available at Book Depository with free delivery worldwide. Field Arithmetic explores Diophantine fields through their absolute Galois groups. The treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. Hardware Implementation of Finite-Field Arithmetic describes algorithms and circuits for executing finite-field operations, including addition, subtraction, multiplication, squaring, exponentiation, and division. The book concludes with a real-world example of a finite-field application--elliptic-curve cryptography. This is an essential.