Kalyan Chakraborty – författare

This book presents cutting-edge research, advanced techniques, and practical applications of Algebra Analysis and Topology. It offers in-depth insights, theoretical developments, and practical applications, showcasing the richness and interdisciplinary nature of algebra, analysis, and topology. The book fosters a deeper understanding of the fundamental principles while also highlighting the latest advancements and emerging trends in these disciplines. Readers are encouraged to apply the theoretical concepts and techniques to solve mathematical problems, engaging with the book''s problem-solving approach. By combining theoretical foundations, practical applications, and interdisciplinary perspectives, this book aims to inspire new avenues of research and contribute to the ongoing development of these dynamic fields.

• Provides a comprehensive and accessible resource that covers a broad range of topics in algebra, analysis, and topology, understanding of the interconnections between these mathematical fields

• Encompasses both classical topics and cutting-edge research areas within algebra, analysis, and topology

• Covers foundational concepts, advanced theories, and their applications in diverse fields such as physics, computer science, engineering, and economics

• Offers sophisticated tools and methodologies to tackle complex problems and deepen the understanding of these disciplines

• Explores how algebra, analysis, and topology intersect with other fields of mathematics and how their concepts and techniques can be applied in related disciplines

It serves as a valuable reference for graduate students, researchers, and mathematicians seeking to deepen their knowledge and engage with the latest advancements in these fundamental branches of mathematics.

This book presents cutting-edge research, advanced techniques, and practical applications of Algebra Analysis and Topology. It offers in-depth insights, theoretical developments, and practical applications, showcasing the richness and interdisciplinary nature of algebra, analysis, and topology. The book fosters a deeper understanding of the fundamental principles while also highlighting the latest advancements and emerging trends in these disciplines. Readers are encouraged to apply the theoretical concepts and techniques to solve mathematical problems, engaging with the book''s problem-solving approach. By combining theoretical foundations, practical applications, and interdisciplinary perspectives, this book aims to inspire new avenues of research and contribute to the ongoing development of these dynamic fields.

• Provides a comprehensive and accessible resource that covers a broad range of topics in algebra, analysis, and topology, understanding of the interconnections between these mathematical fields

• Encompasses both classical topics and cutting-edge research areas within algebra, analysis, and topology

• Covers foundational concepts, advanced theories, and their applications in diverse fields such as physics, computer science, engineering, and economics

• Offers sophisticated tools and methodologies to tackle complex problems and deepen the understanding of these disciplines

• Explores how algebra, analysis, and topology intersect with other fields of mathematics and how their concepts and techniques can be applied in related disciplines

It serves as a valuable reference for graduate students, researchers, and mathematicians seeking to deepen their knowledge and engage with the latest advancements in these fundamental branches of mathematics.

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.

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.