Higher correlations of divisor sums related to primes I: triple correlations

By D. Goldston, C. Yıldırım. 2001

65 citations recorded by the source corpus.

We obtain the triple correlations for a truncated divisor sum related to primes. We also obtain the mixed correlations for this divisor sum when it is summed over the primes, and give some applications to primes in short intervals.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/90d0cfe97cd34f3629713dfda28e993739be09b3

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In Algebra and Number Theory

In Geometry and Topology

Citations in the corpus

Higher correlations of divisor sums related to primes II: variations of the error term in the prime number theorem (2004, background): “In the previous paper of this series [7] we gave the calculation of the correlations of ΛR(n) = ∑ d|n d R μ(d) log(R/d), for n 1, (1.2) and ΛR(n) = 0 if n 0.”
The Gaussian primes contain arbitrarily shaped constellations (2005, unknown): “We could substitute this into (69), which is essentially what is done in [9] (and in the earlier work of Goldston and Yoldorom in [6], [4], [5]).”
A relative Szemerédi theorem (2013, methodology): “This is a strengthening of an earlier theorem used by Tao in his proof that the Gaussian primes contain arbitrarily shaped constellations and, by standard arguments, allows us to deduce the relative Szemerédi theorem.”