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

In: Class Groups of Number Fields and Related Topics

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  • Anupam Saikia

    (Indian Institute of Technology, Department of Mathematics)

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].

Suggested Citation

  • Anupam Saikia, 2020. "Divisibility of Class Number of a Real Cubic or Quadratic Field and Its Fundamental Unit," Springer Books, in: Kalyan Chakraborty & Azizul Hoque & Prem Prakash Pandey (ed.), Class Groups of Number Fields and Related Topics, pages 67-72, Springer.
    • Handle: RePEc:spr:sprchp:978-981-15-1514-9_6
    DOI: 10.1007/978-981-15-1514-9_6
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