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Class Groups of Number Fields and Related Topics

Editors: Chakraborty, Kalyan, Hoque, Azizul, Pandey, Prem Prakash (Eds.)

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  • 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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  • ISBN 978-981-15-1514-9
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Hardcover 77,99 €
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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 researchers to the field will also benefit immensely from the diverse problems discussed. All the contributing authors are leading academicians, scientists, researchers, and scholars.


About the authors

KALYAN CHAKRABORTY is Professor at Harish-Chandra Research Institute (HRI), Allahabad, India, where he also obtained his Ph.D. in Mathematics. Professor Chakraborty was a postdoctoral fellow at IMSc, Chennai, and at Queen’s University, Canada, and a visiting scholar at the University of Paris VI, VII, France; Tokyo Metropolitan University, Japan; Universitá Roma Tre, Italy; The University of Hong Kong, Hong Kong; Northwest University and Shandong University, China; Mahidol University, Thailand; Mandalay University, Myanmar; and many more. His broad area of research is number theory, particularly class groups, Diophantine equations, automorphic forms, arithmetic functions, elliptic curves, and special functions. He has published more than 60 research articles in respected journals and two books on number theory, and has been on the editorial boards of various leading journals. Professor Chakraborty is Vice-President of the Society for Special Functions and their Applications.
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.

Table of contents (16 chapters)

Table of contents (16 chapters)

Buy this book

eBook 64,19 €
price for Spain (gross)
  • ISBN 978-981-15-1514-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 77,99 €
price for Spain (gross)
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Bibliographic Information

Bibliographic Information
Book Title
Class Groups of Number Fields and Related Topics
Editors
  • Kalyan Chakraborty
  • Azizul Hoque
  • Prem Prakash Pandey
Copyright
2020
Publisher
Springer Singapore
Copyright Holder
Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-15-1514-9
DOI
10.1007/978-981-15-1514-9
Hardcover ISBN
978-981-15-1513-2
Edition Number
1
Number of Pages
XII, 178
Number of Illustrations
6 b/w illustrations
Topics

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