Bounded gaps between Gaussian primes

Vatwani, Akshaa

doi:10.1016/j.jnt.2016.07.008

Cited by 10 publications

(14 citation statements)

References 11 publications

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“…More importantly, the techniques of Maynard and Tao has been used by many mathematicians since then. In [1] and [14], this method has been extended to obtain bounded gap between primes in number fields and function fields.…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

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

Darbar,

Mukhopadhyay,

Viswanadham

2017

Preprint

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Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

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

Darbar,

Mukhopadhyay,

Viswanadham

2017

Preprint

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“…In that case, there exist infinitely many pairs of such Gaussian primes where their euclidean distance is bounded by an absolute constant. In 2017, Akshaa Vatwani [3] has conjectured this statement and proved it partially. Aksha's conjectures say that there exist infinitely many Gaussian prime pairs which are bounded by 246.…”

Section: Introductionmentioning

confidence: 95%

“…Before going to the proof we discuss the Gaussian primes with bounded length gaps because they prevent us to make an infinite sequence of Gaussian primes with an unbounded gap. In 2017, Akshaa Vatwani [3] has conjectured that Conjecture 1. Given any integers m 1 and m 2 having the same parity, there are infinitely many pairs of rational primes (p 1 , p 2 ) of the form…”

Section: Proof Of Theoremmentioning

confidence: 99%

A Note on The Gaussian Moat Problem

Das¹

2019

Preprint

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The Gaussian moat problem asks whether it is possible to find an infinite sequence of distinct Gaussian prime numbers such that the difference between consecutive numbers in the sequence is bounded. In this paper, we have proved that the answer is 'No', that is an infinite sequence of distinct Gaussian prime numbers can not be bounded by an absolute constant, for the Gaussian primes p = a 2 + b 2 with a, b = 0. We consider each prime (a, b) as a lattice point on the complex plane and use their properties to prove the main result.

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“…The fact that one can restrict the entire argument to an arithmetic progression also allows one to get some control on the joint distribution of various arithmetic functions. There have been many recent works making use of these flexibilities in the setup of the sieve method, including [58,13,7,21,48,34,3,39,4,14,61,59,46,47,28,5,6,1,32,43,49].…”

Section: Other Applications and Further Readingmentioning

confidence: 99%