AIMS Mathematics, 2019, 4(1): 79-85. doi: 10.3934/Math.2019.1.79.

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On the gap between prime ideals

Mathematical College, Sichuan University, Chengdu 610064, China

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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Keywords ring of integers; quadratic field; cyclotomic field; prime gap; diophantine equations

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


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