Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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NEW BOUNDS FOR FUNDAMENTAL UNITS AND CLASS NUMBERS OF REAL QUADRATIC FIELDS

  • Received : 2020.09.01
  • Accepted : 2021.07.06
  • Published : 2021.09.30
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Abstract

In this paper, we present new bounds on the fundamental units of real quadratic fields ${\mathbb{Q}}({\sqrt{d}})$ using the continued fraction expansion of the integral basis element of the field. Furthermore, we apply these bounds to Dirichlet's class number formula. Consequently, we provide computational advantages to estimate the class numbers of such fields. We also give some numerical examples.

Keywords

Acknowledgement

The authors are very grateful to the referee for careful reading and many invaluable suggestions.

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