Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges

DOI10.1112/plms.12181zbMath1426.11107arXiv1707.01315OpenAlexW3123698023WikidataQ121339196 ScholiaQ121339196MaRDI QIDQ4628461

Kaisa Matomäki, Maksym Radziwiłł, Terence C. Tao

Publication date: 13 March 2019

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.01315

zbMATH Keywords

correlationGoldbach conjectureHardy-Littlewood prime tuples conjecturehigher divisor functiondivisor correlation conjecturehigher order Titchmarsh divisor problemvon Mongoldt function

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Applications of sieve methods (11N36)

Related Items (15)

Moment estimates for the exponential sum with higher divisor functions ⋮ PRIME NUMBERS: AN ALTERNATIVE STUDY USING OVA-ANGULAR ROTATIONS ⋮ On the Hardy–Littlewood–Chowla conjecture on average ⋮ On prime vs. prime power pairs ⋮ Averages of shifted convolution sums for arithmetic functions ⋮ Higher uniformity of arithmetic functions in short intervals I. All intervals ⋮ Correlations of the von Mangoldt and higher divisor functions. II: Divisor correlations in short ranges ⋮ Triple correlations of ternary divisor functions. II ⋮ Enveloping sieve related to the Hardy-Littlewood irreducible tuple conjecture in a function field ⋮ On the asymptotics of the shifted sums of Hecke eigenvalue squares ⋮ Goldbach numbers in short intervals ⋮ Combinatorial identities and Titchmarsh's divisor problem for multiplicative functions ⋮ Fourier uniformity of bounded multiplicative functions in short intervals on average ⋮ Averaged forms of two conjectures of Erdős and Pomerance, and their applications ⋮ Correlations of almost primes

This page was built for publication: Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges