A note on correlations of arithmetic functions

2014/05/04 by Sergei Preobrazhenskiĭ, Preobrazhenskii, Sergei, Tatyana Preobrazhenskaya +1
Mathematics · #Advanced Mathematical Identities #Advanced Mathematical Theories #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1405.0682

openalex publication_date 2014/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we describe weight functions that exhibit a transitional behavior between weak and strong correlation with the Liouville function. We also describe a binary problem which may be considered as an interpolation between Chowla's conjecture for two-point correlations of the Möbius function and the twin prime conjecture, in view of recent parity breaking results of K. Matomäki, M. Radziwiłł and T. Tao.

Related

• On the Chowla and twin primes conjectures over \mathbb F_q[T]
• Statistics of the zeros of L-functions and arithmetic correlations
• Note on the Theory of Correlation Functions
• Prime and Möbius correlations for very short intervals in \mathbbF_q[x]
• General elementary methods meeting elementary properties of correlations