Higher correlations of divisor sums related to primes III: k-correlations

Abstract

We obtain the general k-correlations for a short divisor sum related to primes.

32 pages

References in corpus (2)

• Beyond pair correlation
• On the second moment for primes in an arithmetic progression

Cited by in corpus (24)

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• A relative Szemerédi theorem
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• The Path to Recent Progress on Small Gaps Between Primes
• The Gaussian primes contain arbitrarily shaped constellations
• Primes in Tuples II
• The Hardy--Littlewood--Chowla conjecture in the presence of a Siegel zero
• A Multidimensional Szemerédi Theorem in the primes
• Arithmetic progressions and the primes - El Escorial lectures
• Obstructions to uniformity, and arithmetic patterns in the primes
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• The Green-Tao theorem for Piatetski-Shapiro primes
• Primes in Tuples IV: Density of small gaps between consecutive primes
• Additive combinatorics with a view towards computer science and cryptography: An exposition
• The prime ideals in every class contain arbitrary large truncated classes
• Positive Proportion of Small Gaps Between Consecutive Primes
• Arithmetic progressions of primes in short intervals
• Restriction theory of the Selberg sieve, with applications
• On the connection between the Goldbach conjecture and the Elliott-Halberstam conjecture
• Higher Correlations of Divisor Sums Related to Primes II: Variations of the error term in the prime number theorem
• The Green-Tao theorem for primes of the form $x^2+y^2+1$