東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Linked to FindBook

Google Book

Amazon

博客來

Diophantine m-tuples and elliptic curves

Record Type:	Electronic resources : Monograph/item
Title/Author:	Diophantine m-tuples and elliptic curves/ by Andrej Dujella.
Author:	Dujella, Andrej.
Published:	Cham :Springer Nature Switzerland : : 2024.,
Description:	x, 305 p. :ill., digital ;24 cm.
[NT 15003449]:	Introduction -- Elliptic curves over the rationals -- Elliptic curves induced by Diophantine triples -- Integer points on elliptic curves -- Sets with the property D(n)
Contained By:	Springer Nature eBook
Subject:	Diophantine analysis. -
Online resource:	https://doi.org/10.1007/978-3-031-56724-7
ISBN:	9783031567247

Diophantine m-tuples and elliptic curves
Dujella, Andrej.

Diophantine m-tuples and elliptic curves[electronic resource] /by Andrej Dujella. - Cham :Springer Nature Switzerland :2024. - x, 305 p. :ill., digital ;24 cm. - Developments in mathematics,v. 792197-795X ;. - Developments in mathematics ;v. 79..

Introduction -- Elliptic curves over the rationals -- Elliptic curves induced by Diophantine triples -- Integer points on elliptic curves -- Sets with the property D(n)

This book provides an overview of the main results and problems concerning Diophantine m-tuples, i.e., sets of integers or rationals with the property that the product of any two of them is one less than a square, and their connections with elliptic curves. It presents the contributions of famous mathematicians of the past, like Diophantus, Fermat and Euler, as well as some recent results of the author and his collaborators. The book presents fragments of the history of Diophantine m-tuples, emphasising the connections between Diophantine m-tuples and elliptic curves. It is shown how elliptic curves are used in solving some longstanding problems on Diophantine m-tuples, such as the existence of infinite families of rational Diophantine sextuples. On the other hand, rational Diophantine m-tuples are used to construct elliptic curves with interesting Mordell-Weil groups, including curves of record rank with a given torsion group. The book contains concrete algorithms and advice on how to use the software package PARI/GP for solving computational problems. This book is primarily intended for researchers and graduate students in Diophantine equations and elliptic curves. However, it can be of interest to other mathematicians interested in number theory and arithmetic geometry. The prerequisites are on the level of a standard first course in elementary number theory. Background in elliptic curves, Diophantine equations and Diophantine approximations is provided.

ISBN: 9783031567247

Standard No.: 10.1007/978-3-031-56724-7doiSubjects--Topical Terms:

540536
Diophantine analysis.

LC Class. No.: QA242

Dewey Class. No.: 512.74

Diophantine m-tuples and elliptic curves
LDR:02666nmm a2200337 a 4500 001 2371733
003 DE-He213
005 20240605014247.0
006 m d
007 cr nn 008maaau
008 241127s2024 sz s 0 eng d
020 $a 9783031567247 $q (electronic bk.)
020 $a 9783031567230 $q (paper)
024 7 $a 10.1007/978-3-031-56724-7 $2 doi
035 $a 978-3-031-56724-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA242
072 7 $a PBH $2 bicssc
072 7 $a MAT022000 $2 bisacsh
072 7 $a PBH $2 thema
082 0 4 $a 512.74 $2 23
090 $a QA242 $b .D876 2024
100 1 $a Dujella, Andrej. $3 3717971
245 1 0 $a Diophantine m-tuples and elliptic curves $h [electronic resource] / $c by Andrej Dujella.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2024.
300 $a x, 305 p. : $b ill., digital ; $c 24 cm.
490 1 $a Developments in mathematics, $x 2197-795X ; $v v. 79
505 0 $a Introduction -- Elliptic curves over the rationals -- Elliptic curves induced by Diophantine triples -- Integer points on elliptic curves -- Sets with the property D(n)
520 $a This book provides an overview of the main results and problems concerning Diophantine m-tuples, i.e., sets of integers or rationals with the property that the product of any two of them is one less than a square, and their connections with elliptic curves. It presents the contributions of famous mathematicians of the past, like Diophantus, Fermat and Euler, as well as some recent results of the author and his collaborators. The book presents fragments of the history of Diophantine m-tuples, emphasising the connections between Diophantine m-tuples and elliptic curves. It is shown how elliptic curves are used in solving some longstanding problems on Diophantine m-tuples, such as the existence of infinite families of rational Diophantine sextuples. On the other hand, rational Diophantine m-tuples are used to construct elliptic curves with interesting Mordell-Weil groups, including curves of record rank with a given torsion group. The book contains concrete algorithms and advice on how to use the software package PARI/GP for solving computational problems. This book is primarily intended for researchers and graduate students in Diophantine equations and elliptic curves. However, it can be of interest to other mathematicians interested in number theory and arithmetic geometry. The prerequisites are on the level of a standard first course in elementary number theory. Background in elliptic curves, Diophantine equations and Diophantine approximations is provided.
650 0 $a Diophantine analysis. $3 540536
650 0 $a Curves, Elliptic. $3 540506
650 1 4 $a Number Theory. $3 891078
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Developments in mathematics ; $v v. 79. $3 3717972
856 4 0 $u https://doi.org/10.1007/978-3-031-56724-7
950 $a Mathematics and Statistics (SpringerNature-11649)