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Divisibility of Class Numbers of Quadratic Fields: Qualitative Aspects

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Advances in Mathematical Inequalities and Applications

Part of the book series: Trends in Mathematics ((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.

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Acknowledgements

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

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Authors and Affiliations

  1. Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad, 211019, India

    Kalyan Chakraborty & Azizul Hoque

  2. Malaviya National Institute of Technology Jaipur, Jaipur, 302017, India

    Richa Sharma

Authors
  1. Kalyan Chakraborty
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  2. Azizul Hoque
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  3. Richa Sharma
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Corresponding author

Correspondence to Kalyan Chakraborty .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Anand International College of Engineering, Jaipur, India

    Praveen Agarwal

  2. Department of Mathematics, Victoria University, Melbourne, VIC, Australia

    Silvestru Sever Dragomir

  3. Department of Mathematics, King Saud University, Riyadh, Saudi Arabia

    Mohamed Jleli

  4. Department of Mathematics, King Saud University, Riyadh, Saudi Arabia

    Bessem Samet

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Chakraborty, K., Hoque, A., Sharma, R. (2018). Divisibility of Class Numbers of Quadratic Fields: Qualitative Aspects. In: Agarwal, P., Dragomir, S., Jleli, M., Samet, B. (eds) Advances in Mathematical Inequalities and Applications. Trends in Mathematics. Birkhäuser, Singapore. https://doi.org/10.1007/978-981-13-3013-1_12

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