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Class groups of number fields and related topics. Collected papers presented at the first international conference, ICCGNFRT, Harish-Chandra Research Institute, Allahabad, India, September 4–7, 2017. (English) Zbl 1444.11004
Singapore: Springer (ISBN 978-981-15-1513-2/hbk; 978-981-15-1514-9/ebook). xii, 178 p. (2020).

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Publisher’s 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 researchers to the field will also benefit immensely from the diverse problems discussed. All the contributing authors are leading academicians, scientists, researchers, and scholars.
The articles of this volume will be reviewed individually.
Indexed articles:
Gillibert, Jean; Levin, Aaron, A geometric approach to large class groups: a survey, 1-15 [Zbl 1444.11218]
Komatsu, Toru, On simultaneous divisibility of the class numbers of imaginary quadratic fields, 17-24 [Zbl 1444.11220]
Waldschmidt, Michel, Thue Diophantine equations, 25-41 [Zbl 07220059]
Kawamoto, Fuminori; Kishi, Yasuhiro, A lower bound for the class number of certain real quadratic fields, 43-56 [Zbl 1444.11219]
Srinivas, Kotyada; Subramani, Muthukrishnan, A survey of certain Euclidean number fields, 57-65 [Zbl 1436.11127]
Saikia, Anupam, Divisibility of class number of a real cubic or quadratic field and its fundamental unit, 67-72 [Zbl 1444.11221]
Mihăilescu, Preda, The charm of units I, On the Kummer-Vandiver conjecture. Extended abstract, 73-87 [Zbl 07220063]
Schoof, René, Heights and principal ideals of certain cyclotomic fields, 89-96 [Zbl 07220064]
Chattopadhyay, Jaitra; Roy, Bidisha; Sarkar, Subha; Thangadurai, R., Distribution of residues modulo \(p\) using the Dirichlet’s class number formula, 97-107 [Zbl 1444.11008]
Chakraborty, Debopam, On class number divisibility of number fields and points on elliptic curves, 109-112 [Zbl 1436.11133]
Luca, Florian; Mihăilescu, Preda, Small fields with large class groups, 113-118 [Zbl 07220067]
Ahmed, Md. Helal; Tanti, Jagmohan, Cyclotomic numbers and Jacobi sums: a survey, 119-140 [Zbl 07220068]
Kalita, Himashree; Saikia, Helen K., A pair of quadratic fields with class number divisible by 3, 141-146 [Zbl 1444.11212]
Sharma, Richa, On Lebesgue-Ramanujan-Nagell type equations, 147-161 [Zbl 1447.11053]
Mishra, Mohit, Partial Dedekind zeta values and class numbers of R-D type real quadratic fields, 163-174 [Zbl 07220071]
Louboutin, Stéphane R., On the continued fraction expansions of \(\sqrt{p}\) and \(\sqrt{2p}\) for primes \(p\equiv 3\pmod 4\), 175-178 [Zbl 1442.11015]
MSC:
11-06 Proceedings, conferences, collections, etc. pertaining to number theory
00B25 Proceedings of conferences of miscellaneous specific interest
11R27 Units and factorization
11R29 Class numbers, class groups, discriminants
11R42 Zeta functions and \(L\)-functions of number fields
11D59 Thue-Mahler equations
11G05 Elliptic curves over global fields
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