SU\G(𝔸)/K·U

A higher rank Selberg sieve with an additive twist and applications

M. Ram Murty, Akshaa Vatwani

Type: Article

Publication Date: 2017-03-28

Citations: 3

DOI: https://doi.org/10.7169/facm/1622

Abstract

We develop an axiomatic formulation of the higher rank version of the classical Selberg sieve with an ``additive twist'' and provide asymptotic formulas for the same. As an application of this higher rank sieve, we obtain improvements of results of Heath-Brown and Ho-Tsang on almost prime $k$-tuples.

Locations

  • Functiones et Approximatio Commentarii Mathematici - View
  • Project Euclid (Cornell University) - View - PDF

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Works Cited by This (12)

Action Title Year Authors
+ Opera de Cribro 2010 John Friedlander
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+ An Asymptotic Formula in the Theory of Numbers 1957 C. Hooley
+ On almost prime k-tuples 2006 Kwan-hung Ho
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+ PDF Chat Variants of the Selberg sieve, and bounded intervals containing many primes 2014 DHJ Polymath
+ Almost‐prime <i>k</i> ‐tuples 1997 D. R. Heath‐Brown
+ PDF Chat Small gaps between primes 2014 James Maynard
+ PDF Chat Bounded gaps between primes 2014 Zhang Yitang
+ Bounded length intervals containing two primes and an almost-prime II 2015 James Maynard
+ PDF Chat Bounded Gaps Between Primes of a Special Form 2015 Hongze Li
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+ PDF Chat Primes in tuples I 2009 D. A. Goldston
J. Pintz
C. Y. Yıldırım