In 1986, Ivi\'c and Tenenbaum introduced arithmetic functions with squarefull kernel, which are also called $s$-functions. Later, Erd\H{o}s and Ivi\'c gave an asymptotic estimate on the shifted convolution sums of $s$-functions. Recently, Bergelson and Richter studied the orbits along the prime Omega function in a uniq...
In 1965, Chowla conjectured that the signs of the Liouville function become asymptotically uncorrelated at any fixed collection of distinct shifts. In 2015, Matom\"aki, Radziwi\l\l{} and Tao proved an averaged form of Chowla's conjecture. In 2022, Lichtman proved a variant of this conjecture over primes on average. In...
Let $k\ge1$ be an integer and let $\lambda$ be the Liouville function. In 1965, Chowla gave a conjecture that the values of $\lambda(n+h_1),\dots, \lambda(n+h_k)$ are asymptotically unrelated for any distinct natural numbers $h_1, \dots, h_k$. In this article, motivated by the recent work of Bergelson and Richter on th...
Let $k\ge1$ be an integer and let $\lambda$ be the Liouville function. In 1965, Chowla gave a conjecture that the values of $\lambda(n+h_1),\dots, \lambda(n+h_k)$ are asymptotically unrelated for any distinct natural numbers $h_1, \dots, h_k$. In this article, motivated by the recent work of Bergelson and Richter on th...
Let $k\ge1$ be an integer and let $\lambda$ be the Liouville function. In 1965, Chowla gave a conjecture that the values of $\lambda(n+h_1),\dots, \lambda(n+h_k)$ are asymptotically unrelated for any distinct natural numbers $h_1, \dots, h_k$. In this article, motivated by the recent work of Bergelson and Richter on th...
Biao Wang· 0 citations
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