MARC Record from marc_columbia

LEADER: 03395cam a2200361 a 4500
001 7007463
005 20221130203121.0
008 080825s2008 nyu 000 0 eng
020 $a9780387849225 (hbk.)
020 $a038784922X (hbk.)
024 $a40016254148
035 $a(OCoLC)245561348
035 $a(OCoLC)ocn245561348
035 $a(NNC)7007463
035 $a7007463
040 $aUKM$cUKM$dYDXCP$dCDX$dNNC$dOrLoB-B
050 4 $aQA242$b.J33 2009
082 04 $a513.72$222
082 04 $a512.7 22$222
100 1 $aJacobson, Michael.$0http://id.loc.gov/authorities/names/n88079624
245 10 $aSolving the Pell equation /$cby Michael Jacobson, Hugh Williams.
260 $aNew York ;$aLondon :$bSpringer,$c2008.
263 $a200812
300 $a495 pages ;$c24 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
490 1 $aCMS books in mathematics
505 00 $g1.$tIntroduction -- $g2.$tEarly History of the Pell Equation -- $g3.$tContinued Fractions -- $g4.$tQuadratic Number Fields -- $g5.$tIdeals and Continued Fractions -- $g6.$tSome Special Pell Equations -- $g7.$tThe Ideal Class Group -- $g8.$tThe Analytic Class Number Formula -- $g9.$tSome Additional Analytic Results -- $g10.$tSome Computational Techniques -- $g11.$t(f,p) Representations of [actual symbol not reproducible]-ideals -- $g12.$tCompact Representations -- $g13.$tThe Subexponential Method -- $g14.$tApplications to Cryptography -- $g15.$tUnconditional Verification of the Regulator and the Class Number -- $g16.$tPrincipal Ideal Testing in [actual symbol not reproducible] -- $g17.$tConclusion.
520 1 $a"Pell'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."--BOOK JACKET.
650 0 $aPell's equation.$0http://id.loc.gov/authorities/subjects/sh2002004493
700 1 $aWilliams, Hugh.$0http://id.loc.gov/authorities/names/n78083920
830 0 $aCMS books in mathematics.$0http://id.loc.gov/authorities/names/n99830842
852 00 $bmat$hQA242$i.J33 2009g