6 citations · 17 across the 15 of their papers we have counts for
15 papers
Maximising the number of solutions to linear equations
Žarko Ranđelović, Xuancheng Shao, Max Wenqiang Xu +2
We study the asymptotically maximal possible number of integer solutions to the linear equation with a fixed choice of and variables $x, y,…
Distribution of random multiplicative functions in short intervals, with proper normalization
Adam J. Harper, Kannan Soundararajan, Max Wenqiang Xu
We determine the limiting distribution of partial sums of a Steinhaus random multiplicative function over short intervals , where $y \rightar…
Extreme values of Dirichlet polynomials with multiplicative coefficients
Max Wenqiang Xu, Daodao Yang
We study extreme values of Dirichlet polynomials with multiplicative coefficients, namely \[D_N(t) : = D_{f,\, N}(t)= \frac{1}{\sqrt{N}} \sum_{n\leqslant N} f(n) n^{it}, \] where $…
Better than square-root cancellation for random multiplicative functions
Max Wenqiang Xu
We investigate when the better than square-root cancellation phenomenon exists for , where and is a random multiplicative functio…
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}{(…
Discrepancy in modular arithmetic progressions
Jacob Fox, Max Wenqiang Xu, Yunkun Zhou
Celebrated theorems of Roth and of Matoušek and Spencer together show that the discrepancy of arithmetic progressions in the first positive integers is . We study t…
Mixing time of fractional random walk on finite fields
Jimmy He, Huy Tuan Pham, Max Wenqiang Xu
We study a random walk on defined by if , and if , where are inde…
Multicolor list Ramsey numbers grow exponentially
Jacob Fox, Xiaoyu He, Sammy Luo +1
The list Ramsey number , recently introduced by Alon, Bucić, Kalvari, Kuperwasser, and Szabó, is a list-coloring variant of the classical Ramsey number. They showed…
A note on the Erdős distinct subset sums problem
Quentin Dubroff, Jacob Fox, Max Wenqiang Xu
We present two short proofs giving the best known asymptotic lower bound for the maximum element in a set of positive integers with distinct subset sums.
Irreducibility of random polynomials of bounded degree
Huy Tuan Pham, Max Wenqiang Xu
It is known that random monic integral polynomials of bounded degree and integral coefficients distributed uniformly and independently in are irreducible over $\mathbb…