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arXiv · 1711.01949

Bounded gaps between product of two primes in imaginary quadratic number fields

Pranendu Darbar·Anirban Mukhopadhyay·G. K. Viswanadham
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Abstract

We study the gaps between products of two primes in imaginary quadratic number fields using a combination of the methods of Goldston-Graham-Pintz-Yildirim \cite{GGPY}, and Maynard \cite{MAY}. An important consequence of our main theorem is existence of infinitely many pairs $α_1, α_2$ which are product of two primes in the imaginary quadratic field $K$ such that $|σ(α_1-α_2)|\leq 2$ for all embedding $σ$ of $K$ if the class number of $K$ is one and $|σ(α_1-α_2)|\leq 8$ for all embedding $σ$ of $K$ if the class number of $K$ is two.

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Pranendu Darbar, Anirban Mukhopadhyay, G. K. Viswanadham. 2020-08-08. Bounded gaps between product of two primes in imaginary quadratic number fields. https://arxiv.org/abs/1711.01949

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