Divisibility of Class Number of a Real Cubic or Quadratic Field and Its Fundamental Unit

Anupam Saikia ()
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Anupam Saikia: Indian Institute of Technology, Department of Mathematics

A chapter in Class Groups of Number Fields and Related Topics, 2020, pp 67-72 from Springer

Abstract: Abstract This article presents joint work with Debopam Chakraborty [1] on exploring relation between congruence properties of the fundamental unit of a pure cubic field and its class number. We show that 3-divisibility of the class number is related to certain congruences satisfied by the fundamental unit. Then we prove certain congruences for the fundamental unit of a real quadratic field of odd class number which are stronger than the ones in [6] and in [1].

Keywords: Fundamental unit; Class number; Primary 11R16; Secondary 11R27; 11R29; 11R11 (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-15-1514-9_6

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DOI: 10.1007/978-981-15-1514-9_6

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