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Title Class groups of number fields and related topics / Kalyan Chakraborty, Azizul Hoque, Prem Prakash Pandey, editors
Published Singapore : Springer, [2020]
©2020

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Description 1 online resource (xii, 172 pages) : illustrations
Contents A geometric approach to large class groups: a survey -- On simultaneous divisibility of the class numbers of imaginary quadratic fields -- Thue Diophantine Equations -- A lower bound for the class number of certain real quadratic fields -- A survey of certain Euclidean number fields -- Divisibility of class number of a real cubic or quadratic field and its fundamental unit -- The charm of units I, on the Kummer-Vandiver conjecture. Extended abstract -- Heights and principal ideals of certain cyclotomic fields -- Distribution of residues modulo p using the Dirichlet's class number formula -- On class number divisibility of number fields and points on elliptic curves -- Small fields with large class groups -- Cyclotomic numbers and Jacobi sums: a survey -- A pair of quadratic fields with class number divisible by 3 -- On Lebesgue-Ramanujan-Nagell type equations -- Partial Dedekind zeta values and class numbers of R-D type real quadratic fields -- On the continued fraction expansions of sqrtp and sqrt2p for primes pequiv38mu(mod6mu4)
Summary "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"--Publisher's description
Bibliography Includes bibliographical references
Notes Online resource; title from resource home page (ProQuest Ebook Central, viewed April 14, 2020)
Subject Class groups (Mathematics)
Class groups (Mathematics)
Form Electronic book
Author Chakraborty, Kalyan, editor
Hoque, Azizul, editor
Pandey, Prem Prakash, editor
International Conference on Class Groups of Number Fields and Related Topics (2017 : Allahabad, India)
ISBN 9789811515149
981151514X