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Class groups of number fields and re...

Chakraborty, Kalyan.

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Class groups of number fields and related topics

Record Type:	Electronic resources : Monograph/item
Title/Author:	Class groups of number fields and related topics/ edited by Kalyan Chakraborty, Azizul Hoque, Prem Prakash Pandey.
other author:	Chakraborty, Kalyan.
Published:	Singapore :Springer Singapore : : 2020.,
Description:	xii, 178 p. :ill., digital ;24 cm.
[NT 15003449]:	1. A Geometric Approach to Large Class Groups: A Survey -- 2. On Simultaneous Divisibility of the Class Numbers of Imaginary Quadratic Fields -- 3. Thue Diophantine Equations: A Survey -- 4. A Lower Bound for the Class Number of Certain Real Quadratic Fields -- 5. A Survey of Certain Euclidean Number Fields -- Divisibility of Class Number of a Real Cubic or Quadratic Field and Its Fundamental Unit -- 6. Heights and Principal Ideals of Certain Cyclotomic Fields -- 7. Distribution of Residues Modulo p using the Dirichlet's Class Number Formula -- 8. On the Class Number Divisibility of Number Fields and Points on Elliptic Curves -- 9. Small Fields with Large Class Numbers -- 10. On the Kummer-Vandiver Conjecture: An Extended Abstract -- 11. Cyclotomic Numbers and Jacobi Sums: A Survey -- 12. On Lebesgue-Ramanujan-Nagell Type Equations -- 13. Partial Zeta Values and Class Numbers of R-D Type Real Quadratic Fields -- 14. A Pair of Quadratic Fields with Class Number Divisible by 3.
Contained By:	Springer eBooks
Subject:	Class groups (Mathematics) -
Online resource:	https://doi.org/10.1007/978-981-15-1514-9
ISBN:	9789811515149

Class groups of number fields and related topics
Class groups of number fields and related topics[electronic resource] /edited by Kalyan Chakraborty, Azizul Hoque, Prem Prakash Pandey. - Singapore :Springer Singapore :2020. - xii, 178 p. :ill., digital ;24 cm.

1. A Geometric Approach to Large Class Groups: A Survey -- 2. On Simultaneous Divisibility of the Class Numbers of Imaginary Quadratic Fields -- 3. Thue Diophantine Equations: A Survey -- 4. A Lower Bound for the Class Number of Certain Real Quadratic Fields -- 5. A Survey of Certain Euclidean Number Fields -- Divisibility of Class Number of a Real Cubic or Quadratic Field and Its Fundamental Unit -- 6. Heights and Principal Ideals of Certain Cyclotomic Fields -- 7. Distribution of Residues Modulo p using the Dirichlet's Class Number Formula -- 8. On the Class Number Divisibility of Number Fields and Points on Elliptic Curves -- 9. Small Fields with Large Class Numbers -- 10. On the Kummer-Vandiver Conjecture: An Extended Abstract -- 11. Cyclotomic Numbers and Jacobi Sums: A Survey -- 12. On Lebesgue-Ramanujan-Nagell Type Equations -- 13. Partial Zeta Values and Class Numbers of R-D Type Real Quadratic Fields -- 14. A Pair of Quadratic Fields with Class Number Divisible by 3.

This book gathers original research papers and survey articles presented at the "International Conference on Class Groups of Number Fields and Related Topics," held at Harish-Chandra Research Institute, Allahabad, India, on September 4-7, 2017. It discusses the fundamental research problems that arise in the study of class groups of number fields and introduces new techniques and tools to study these problems. Topics in this book include class groups and class numbers of number fields, units, the Kummer-Vandiver conjecture, class number one problem, Diophantine equations, Thue equations, continued fractions, Euclidean number fields, heights, rational torsion points on elliptic curves, cyclotomic numbers, Jacobi sums, and Dedekind zeta values. This book is a valuable resource for undergraduate and graduate students of mathematics as well as researchers interested in class groups of number fields and their connections to other branches of mathematics. New researchers to the field will also benefit immensely from the diverse problems discussed. All the contributing authors are leading academicians, scientists, researchers, and scholars.

ISBN: 9789811515149

Standard No.: 10.1007/978-981-15-1514-9doiSubjects--Topical Terms:

726458
Class groups (Mathematics)

LC Class. No.: QA247 / .C537 2020

Dewey Class. No.: 512.74

Class groups of number fields and related topics
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245 0 0 $a Class groups of number fields and related topics $h [electronic resource] / $c edited by Kalyan Chakraborty, Azizul Hoque, Prem Prakash Pandey.
260 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2020.
300 $a xii, 178 p. : $b ill., digital ; $c 24 cm.
505 0 $a 1. A Geometric Approach to Large Class Groups: A Survey -- 2. On Simultaneous Divisibility of the Class Numbers of Imaginary Quadratic Fields -- 3. Thue Diophantine Equations: A Survey -- 4. A Lower Bound for the Class Number of Certain Real Quadratic Fields -- 5. A Survey of Certain Euclidean Number Fields -- Divisibility of Class Number of a Real Cubic or Quadratic Field and Its Fundamental Unit -- 6. Heights and Principal Ideals of Certain Cyclotomic Fields -- 7. Distribution of Residues Modulo p using the Dirichlet's Class Number Formula -- 8. On the Class Number Divisibility of Number Fields and Points on Elliptic Curves -- 9. Small Fields with Large Class Numbers -- 10. On the Kummer-Vandiver Conjecture: An Extended Abstract -- 11. Cyclotomic Numbers and Jacobi Sums: A Survey -- 12. On Lebesgue-Ramanujan-Nagell Type Equations -- 13. Partial Zeta Values and Class Numbers of R-D Type Real Quadratic Fields -- 14. A Pair of Quadratic Fields with Class Number Divisible by 3.
520 $a This book gathers original research papers and survey articles presented at the "International Conference on Class Groups of Number Fields and Related Topics," held at Harish-Chandra Research Institute, Allahabad, India, on September 4-7, 2017. It discusses the fundamental research problems that arise in the study of class groups of number fields and introduces new techniques and tools to study these problems. Topics in this book include class groups and class numbers of number fields, units, the Kummer-Vandiver conjecture, class number one problem, Diophantine equations, Thue equations, continued fractions, Euclidean number fields, heights, rational torsion points on elliptic curves, cyclotomic numbers, Jacobi sums, and Dedekind zeta values. This book is a valuable resource for undergraduate and graduate students of mathematics as well as researchers interested in class groups of number fields and their connections to other branches of mathematics. New researchers to the field will also benefit immensely from the diverse problems discussed. All the contributing authors are leading academicians, scientists, researchers, and scholars.
650 0 $a Class groups (Mathematics) $3 726458
650 1 4 $a Number Theory. $3 891078
650 2 4 $a Group Theory and Generalizations. $3 893889
650 2 4 $a Ordinary Differential Equations. $3 891264
650 2 4 $a Field Theory and Polynomials. $3 891077
700 1 $a Chakraborty, Kalyan. $3 3447647
700 1 $a Hoque, Azizul. $3 3447648
700 1 $a Pandey, Prem Prakash. $3 3447649
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
856 4 0 $u https://doi.org/10.1007/978-981-15-1514-9
950 $a Mathematics and Statistics (Springer-11649)