Research article

On the gap between prime ideals

  • Received: 18 December 2018 Accepted: 09 January 2019 Published: 16 January 2019
  • MSC : 11R04, 11D99

  • We define a gap function to measure the difference of two distinct prime ideals in a given number field. In this paper, we determine all quadratic fields and cyclotomic fields satisfying the condition: there exist two distinct prime ideals whose gap is 1.

    Citation: Tianyu Ni. On the gap between prime ideals[J]. AIMS Mathematics, 2019, 4(1): 79-85. doi: 10.3934/Math.2019.1.79

    Related Papers:

  • We define a gap function to measure the difference of two distinct prime ideals in a given number field. In this paper, we determine all quadratic fields and cyclotomic fields satisfying the condition: there exist two distinct prime ideals whose gap is 1.


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    [1] J.S. Milne, Algebraic number theory, Lecture Notes, 1998. Available from: http://www.jmilne.org/math/CourseNotes/ant.html.
    [2] J. Neukirch, Algebraic number theory, Berlin: Springer-Verlag, 1999.
    [3] P. Mihäilescu, Primary cyclotomic units and a proof of Catalan's conjecture, J. Reine Angew. Math., 572 (2004), 167-195. doi: 10.1515/crll.2004.048
    [4] T. Metsänkylä, Catalan's conjecture: Another old Diophantine problem solved, B. Am. Math. Soc., 41 (2004), 43-57.
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  • © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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