MARC Record from harvard_bibliographic_metadata

LEADER: 02941cam a22003378a 4500
001 011820864-0
005 20140910154239.0
008 080825s2009 nyu b 001 0 eng
015 $aGBA8A5282$2bnb
016 7 $a014707948$2Uk
020 $a9780387849225 (hbk.)
020 $a038784922X (hbk.)
035 0 $aocn245561348
040 $aUKM$cUKM$dYDXCP$dCDX
050 4 $aQA242$b.J33 2009
082 04 $a513.72$222
082 04 $a512.7 22$222
100 1 $aJacobson, Michael J.
245 10 $aSolving the Pell equation /$cMichael J. Jacobson, Jr., Hugh C. Williams.
260 $aNew York ;$aLondon :$bSpringer,$cc2009.
300 $axx, 495 p. ;$c25 cm.
440 0 $aCMS books in mathematics
504 $aIncludes bibliographical references (p. [461]-488) and index.
505 0 $aEarly History of the Pell Equation -- Continued Fractions -- Quadratic Number Fields -- Ideals and Continued Fractions -- Some Special Pell Equations -- The Ideal Class Group -- The Analytic Class Number Formula -- Some Additional Analytic Results -- Some Computational Techniques -- (f, p) Representations of -ideals -- Compact Representations -- The Subexponential Method -- Applications to Cryptography -- Unconditional Verification of the Regulator and the Class Number -- Principal Ideal Testing in -- Conclusion.
520 $aPell's equation is a very simple, yet fundamental Diophantine equation which is believed to have been known to mathematicians for over 2000 years. Because of its popularity, the Pell equation is often discussed in textbooks and recreational books concerning elementary number theory, but usually not in much depth. This book provides a modern and deeper approach to the problem of solving the Pell equation. The main component of this will be computational techniques, but in the process of deriving these it will be necessary to develop the corresponding theory. One objective of this book is to provide a less intimidating introduction for senior undergraduates and others with the same level of preparedness to the delights of algebraic number theory through the medium of a mathematical object that has fascinated people since the time of Archimedes. To achieve this, this work is made accessible to anyone with some knowledge of elementary number theory and abstract algebra. Many references and notes are provided for those who wish to follow up on various topics, and the authors also describe some rather surprising applications to cryptography. The intended audience is number theorists, both professional and amateur, and students, but we wish to emphasize that this is not intended to be a textbook; its focus is much too narrow for that. It could, however be used as supplementary reading for students enrolled in a second course in number theory.
650 0 $aPell's equation.
650 0 $aMathematics.
650 0 $aNumber theory.
700 1 $aWilliams, Hugh C.
988 $a20090203
906 $0OCLC