國立高雄大學圖資館 |

Language: English

Back

Pillars of transcendental number theory

Natarajan, Saradha.

Pillars of transcendental number theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	Pillars of transcendental number theoryby Saradha Natarajan, Ravindranathan Thangadurai.
Author:	Natarajan, Saradha.
other author:	Thangadurai, Ravindranathan.
Published:	Singapore :Springer Singapore :2020.
Description:	xvii, 174 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Number theory.
Online resource:	https://doi.org/10.1007/978-981-15-4155-1
ISBN:	9789811541551$q(electronic bk.)

Pillars of transcendental number theory
Natarajan, Saradha.

Pillars of transcendental number theory[electronic resource] /by Saradha Natarajan, Ravindranathan Thangadurai. - Singapore :Springer Singapore :2020. - xvii, 174 p. :ill., digital ;24 cm.

1. Preliminaries -- 2. e and pi are Transcendental -- 3. Theorem of Hermite-Lindemann-Weierstrass -- 4. Theorem of Gelfond and Schneider -- 5. Extensions due to Ramachandra -- 6. Diophantine Approximation and Transcendence -- 7. Roth's Theorem -- 8. Baker's Theorems and some Applications -- 9. Ground Work for the Proof of Baker's theorem -- 10. Proof of Baker's Theorem -- 11. Subspace Theorem and Some Applications.

This book deals with the development of Diophantine problems starting with Thue's path breaking result and culminating in Roth's theorem with applications. It discusses classical results including Hermite-Lindemann-Weierstrass theorem, Gelfond-Schneider theorem, Schmidt's subspace theorem and more. It also includes two theorems of Ramachandra which are not widely known and other interesting results derived on the values of Weierstrass elliptic function. Given the constantly growing number of applications of linear forms in logarithms, it is becoming increasingly important for any student wanting to work in this area to know the proofs of Baker's original results. This book presents Baker's original results in a format suitable for graduate students, with a focus on presenting the content in an accessible and simple manner. Each student-friendly chapter concludes with selected problems in the form of "Exercises" and interesting information presented as "Notes," intended to spark readers' curiosity.

ISBN: 9789811541551$q(electronic bk.)

Standard No.: 10.1007/978-981-15-4155-1doiSubjects--Topical Terms:

189521
Number theory.

LC Class. No.: QA241 / .N383 2020

Dewey Class. No.: 512.7

Pillars of transcendental number theory
LDR:02419nmm a2200325 a 4500 001 572074
003 DE-He213
005 20200818094956.0
006 m d
007 cr nn 008maaau
008 200922s2020 si s 0 eng d
020 $a 9789811541551$q(electronic bk.)
020 $a 9789811541544$q(paper)
024 7 $a 10.1007/978-981-15-4155-1 $2 doi
035 $a 978-981-15-4155-1
040 $a GP $c GP
041 0 $a eng
050 4 $a QA241 $b .N383 2020
072 7 $a PBH $2 bicssc
072 7 $a MAT022000 $2 bisacsh
072 7 $a PBH $2 thema
082 0 4 $a 512.7 $2 23
090 $a QA241 $b .N273 2020
100 1 $a Natarajan, Saradha. $3 858971
245 1 0 $a Pillars of transcendental number theory $h [electronic resource] / $c by Saradha Natarajan, Ravindranathan Thangadurai.
260 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2020.
300 $a xvii, 174 p. : $b ill., digital ; $c 24 cm.
505 0 $a 1. Preliminaries -- 2. e and pi are Transcendental -- 3. Theorem of Hermite-Lindemann-Weierstrass -- 4. Theorem of Gelfond and Schneider -- 5. Extensions due to Ramachandra -- 6. Diophantine Approximation and Transcendence -- 7. Roth's Theorem -- 8. Baker's Theorems and some Applications -- 9. Ground Work for the Proof of Baker's theorem -- 10. Proof of Baker's Theorem -- 11. Subspace Theorem and Some Applications.
520 $a This book deals with the development of Diophantine problems starting with Thue's path breaking result and culminating in Roth's theorem with applications. It discusses classical results including Hermite-Lindemann-Weierstrass theorem, Gelfond-Schneider theorem, Schmidt's subspace theorem and more. It also includes two theorems of Ramachandra which are not widely known and other interesting results derived on the values of Weierstrass elliptic function. Given the constantly growing number of applications of linear forms in logarithms, it is becoming increasingly important for any student wanting to work in this area to know the proofs of Baker's original results. This book presents Baker's original results in a format suitable for graduate students, with a focus on presenting the content in an accessible and simple manner. Each student-friendly chapter concludes with selected problems in the form of "Exercises" and interesting information presented as "Notes," intended to spark readers' curiosity.
650 0 $a Number theory. $3 189521
650 1 4 $a Number Theory. $3 274059
650 2 4 $a Real Functions. $3 273779
700 1 $a Thangadurai, Ravindranathan. $3 858972
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
856 4 0 $u https://doi.org/10.1007/978-981-15-4155-1
950 $a Mathematics and Statistics (Springer-11649)