6 citations · 17 across the 15 of their papers we have counts for
6 papers · 1 filter
Central limit theorems for random multiplicative functions
Kannan Soundararajan, Max Wenqiang Xu
A Steinhaus random multiplicative function is a completely multiplicative function obtained by setting its values on primes to be independent random variables distribute…
A polynomial with a root mod for every has a real root
Rodrigo Angelo, Max Wenqiang Xu
We prove that if a polynomial has a root mod for every large prime , then it has a real root. As an application, we show that the primes can't be covered by finitely many po…
Partial sums of typical multiplicative functions over short moving intervals
Mayank Pandey, Victor Y. Wang, Max Wenqiang Xu
We prove that the -th positive integer moment of partial sums of Steinhaus random multiplicative functions over the interval matches the corresponding Gaussian moment…
On a Turán conjecture and random multiplicative functions
Rodrigo Angelo, Max Wenqiang Xu
We show that if is the random completely multiplicative function, the probability that is positive for every is at least , while a…
On the random Chowla conjecture
Oleksiy Klurman, Ilya D. Shkredov, Max Wenqiang Xu
We show that for a Steinhaus random multiplicative function and any polynomial of which is not of the form $…
On product sets of arithmetic progressions
Max Wenqiang Xu, Yunkun Zhou
We prove that the size of the product set of any finite arithmetic progression satisfies \[|\mathcal A \cdot \mathcal A| \ge \frac{|\mathcal A|^2}{(…