Overview
- Presents geometrical and classical techniques to study the class groups of number fields
- Features a chapter on Kummer–Vandiver conjecture
- Explores various techniques to work toward Gauss class number one problem
- Includes a survey on Lebesgue–Ramanujan–Nagell type equations
- Provides a rich history of cyclotomic numbers and Jacobi sums
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Table of contents (16 chapters)
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Front Matter
Keywords
About this book
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 researchersto the field will also benefit immensely from the diverse problems discussed. All the contributing authors are leading academicians, scientists, researchers, and scholars.
Editors and Affiliations
About the editors
AZIZUL HOQUE is a national postdoctoral fellow at Harish-Chandra Research Institute (HRI), Allahabad. He earned his Ph.D. in Pure Mathematics from Gauhati University, Guwahati, in 2015. Before joining HRI, Dr. Hoque was Assistant Professor at the Regional Institute of Science and Technology, Meghalaya, and at the University of Science and Technology, Meghalaya. He has visited Hong Kong University, Hong Kong; Northwest University, China; Shandong University, China; Mahidol University, Thailand; and many more. His research has mostly revolved around class groups, Diophantine equations, elliptic curves, zeta values, and related topics, and he has published a considerable number of papers in respected journals. He has been involved in a number of conferences and received numerous national and international grants.
PREM PRAKASH PANDEY is Assistant Professor at the Indian Institute of Science Education and Research (IISER) Berhampur, Odisha. Before that, he was a postdoctoral fellow at HRI, Allahabad, and NISER Bhubaneswar, Odisha. After completing his Ph.D. at the Institute of Mathematical Sciences (IMSc), Chennai, he spent a couple of years at Chennai Mathematical Institute (CMI), Chennai, as a visiting scholar. Dr. Pandey's interests include class groups of number fields, annihilators of class groups, Diophantine equations, and related topics. During his time at HRI, he worked on divisibility problems for class numbers of quadratic fields with Dr. Hoque and Prof. Chakraborty.
Bibliographic Information
Book Title: Class Groups of Number Fields and Related Topics
Editors: Kalyan Chakraborty, Azizul Hoque, Prem Prakash Pandey
DOI: https://doi.org/10.1007/978-981-15-1514-9
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020
Hardcover ISBN: 978-981-15-1513-2Published: 18 January 2020
Softcover ISBN: 978-981-15-1516-3Published: 18 January 2021
eBook ISBN: 978-981-15-1514-9Published: 17 January 2020
Edition Number: 1
Number of Pages: XII, 178
Number of Illustrations: 6 b/w illustrations
Topics: Number Theory, Group Theory and Generalizations, Ordinary Differential Equations, Field Theory and Polynomials