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Full Description
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.
Contents
1. A Geometric Approach to Large Class Groups: A Survey.- 2. On Simultaneous Divisibility of the Class Numbers of Imaginary Quadratic Fields.- 3. Thue Diophantine Equations: A Survey.- 4. A Lower Bound for the Class Number of Certain Real Quadratic Fields.- 5. A Survey of Certain Euclidean Number Fields.- Divisibility of Class Number of a Real Cubic or Quadratic Field and Its Fundamental Unit.- 6. Heights and Principal Ideals of Certain Cyclotomic Fields.- 7. Distribution of Residues Modulo p using the Dirichlet's Class Number Formula.- 8. On the Class Number Divisibility of Number Fields and Points on Elliptic Curves.- 9. Small Fields with Large Class Numbers.- 10. On the Kummer-Vandiver Conjecture: An Extended Abstract.- 11. Cyclotomic Numbers and Jacobi Sums: A Survey.- 12. On Lebesgue-Ramanujan-Nagell Type Equations.- 13. Partial Zeta Values and Class Numbers of R-D Type Real Quadratic Fields.- 14. A Pair of Quadratic Fields with Class Number Divisible by 3.
