Bulletin of the Korean Mathematical Society (대한수학회보)

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PRIME-PRODUCING POLYNOMIALS RELATED TO CLASS NUMBER ONE PROBLEM OF NUMBER FIELDS

  • Jun Ho Lee (Department of Mathematics Education Mokpo National University)
  • Received : 2022.02.03
  • Accepted : 2022.12.22
  • Published : 2023.03.31
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Abstract

First, we recall the results for prime-producing polynomials related to class number one problem of quadratic fields. Next, we give the relation between prime-producing cubic polynomials and class number one problem of the simplest cubic fields and then present the conjecture for the relations. Finally, we numerically compare the ratios producing prime values for several polynomials in some interval.

Keywords

Acknowledgement

The author sincerely thanks the referees for their valuable comments which improved the original version of this manuscript.

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