Bounded gaps between Gaussian primes
| Autor: | Akshaa Vatwani |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Algebra and Number Theory Gaussian moat Gaussian integer 010102 general mathematics Prime number Table of Gaussian integer factorizations 010103 numerical & computational mathematics 01 natural sciences symbols.namesake Prime quadruplet symbols Unique prime Dirichlet's theorem on arithmetic progressions 0101 mathematics Idoneal number Mathematics |
| Zdroj: | Journal of Number Theory. 171:449-473 |
| ISSN: | 0022-314X |
| Popis: | We show that there are infinitely many distinct rational primes of the form p 1 = a 2 + b 2 and p 2 = a 2 + ( b + h ) 2 , with a , b , h integers, such that | h | ≤ 246 . We do this by viewing a Gaussian prime c + d i as a lattice point ( c , d ) in R 2 and showing that there are infinitely many pairs of distinct Gaussian primes ( c 1 , d 1 ) and ( c 2 , d 2 ) such that the Euclidean distance between them is bounded by 246. Our method, motivated by the work of Maynard [9] and the Polymath project [13] , is applicable to the wider setting of imaginary quadratic fields with class number 1 and yields better results than those previously obtained for gaps between primes in the corresponding number rings. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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