Class Groups of Number Fields and Related Topics

This book collects original research papers and survey articles presented at two conferences on the same theme: the International Conference on Class Groups of Number Fields and Related Topics, held at Kerala School of Mathematics, Kozhikode, Kerala, India, from 21–24 October 2021 and then from 21–24 November 2022. It presents the fundamental research problems that arise in the study of class groups of number fields and related areas. The book also covers some new techniques and tools to study these problems. Topics in this book include class groups of number fields, units, Ankeny–Artin–Chowla conjecture, Iwasawa theory, elliptic curves, Diophantine equations, partition functions, Diophantine tuples, congruent numbers, Carmichael ideals in a number field and their connection with class groups.

This book will be a valuable resource for graduate students and researchers in mathematics interested in class groups of number fields and their connections to other branches of mathematics. It also attracts new researchers to the field and young researchers will benefit immensely from the diverse problems discussed in this book. All the contributing authors are leading academicians, scientists and profound researchers. This book is dedicated to Prof. Michel Waldschmidt, a renowned French number theorist, on his 75th birthday.

Kalyan Chakraborty is Senior Professor at SRM University AP, Amravati, Andhra Pradesh. Earlier, he was Professor at Harish-Chandra Research Institute (HRI), Allahabad, Uttar Pradesh, India, for more than two decades. He obtained his PhD in Mathematics from HRI. He also has been a Post-Doctoral Fellow at the Institute of Mathematical Sciences, Chennai, and at Queen’s University, Canada. He visited the University of Paris VI, VII, Paris; Tokyo Metropolitan University, Kinki University, Kyoto Sangyo University and Waseda University, Japan; Universitá Roma Tre, Italy; University of Hong Kong, Hong Kong; Northwest University, Shangdong University and Shangluo University, China; Mahidol University, Thailand; Mandalaya University, Myanmar; Eötvös Lor’and University, Budapest; and many more. The broad area of his research lies in algebraic number theory and analytic number theory. In addition, his research areas include class groups of numbers fields, Diophantine equations, automorphic forms, arithmetic functions, elliptic curves, cryptography and special functions. With more than 80 research articles published in reputed journals, he has published three books on number theory. A Vice-President of the Society for Special Functions & their Applications (SSFA), he has guided more than 10 PhD students and has been on the editorial board of some reputed journals.

Azizul Hoque is Assistant Professor at Rangapara College, Gauhati University, Assam, India. Earlier, he was a Post-Doctoral Fellow at Harish-Chandra Research Institute (HRI), Allahabad. He earned his Ph.D. in mathematics from Gauhati University, Guwahati, in 2015. Before joining HRI, he was Assistant Professor at the Regional Institute of Science and Technology, Meghalaya, and at University of Science and Technology, Meghalay. He visited the University of Hong Kong, Hong Kong; Northwest University, China; Shangluo University, China; Mahidol University, Thailand; Mandalaya University, Myanmar; and other places. His broad research area lies in algebraic number theory. His research interests include class groups of numbers fields, Diophantine equations, elliptic curves, zeta values and related topics. He has published a considerable number of papers in national and international journals. He has been involved in a number of conferences and has received numerous national and international grants.

Prem Prakash Pandey is Assistant Professor at the Indian Institute of Science Education and Research (IISER) Berhampur, Odisha. Earlier, he was a Post-Doctoral Fellow at Harish-Chandra Research Institute (HRI), Allahabad, and at NISER Bhubaneswar, Odisha, India. He did his Ph.D. from the Institute of Mathematical Sciences, Chennai, India. After his Ph.D., he spent a couple of years at Chennai Mathematical Institute as Visiting Faculty. He has also spent some time at the Hausdorff Centre of Mathematics, Bonn, and Gottingen University, in Germany. His interests include class groups of number fields, annihilators of class groups, Diophantine equations and related topics. He is very much interested in the contribution of prime ideals of different degrees in the class groups.