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Divisibility of Class Numbers of Quadratic Fields: Qualitative Aspects

  • Kalyan ChakrabortyEmail author
  • Azizul Hoque
  • Richa Sharma
Chapter
Part of the Trends in Mathematics book series (TM)

Abstract

Class numbers of quadratic fields have been the object of attention for many years, and there exist a large number of interesting results. This is a survey aimed at reviewing results concerning the divisibility of class numbers of both real and imaginary quadratic fields. More precisely, to review the question ‘do there exist infinitely many real (respectively imaginary) quadratic fields whose class numbers are divisible by a given integer?’ This survey also contains the current status of a quantitative version of this question.

Keywords

Quadratic fields Discriminant Class number Hilbert class field 

2010 Mathematics Subject Classification

Primary: 11R29 Secondary: 11R11 

Notes

Acknowledgements

A. Hoque is supported by SERB N-PDF scheme (PDF/2017/001958), Government of India.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Kalyan Chakraborty
    • 1
    Email author
  • Azizul Hoque
    • 1
  • Richa Sharma
    • 2
  1. 1.Harish-Chandra Research InstituteJhunsi, AllahabadIndia
  2. 2.Malaviya National Institute of Technology JaipurJaipurIndia

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