Search Results - "Wenqiang Xu, Max"

Universality for Low-Degree Factors of Random Polynomials over Finite Fields by He, Jimmy, Tuan Pham, Huy, Wenqiang Xu, Max

“…Abstract We show that the counts of low-degree irreducible factors of a random polynomial $f$ over $\mathbb {F}_q$ with independent but nonuniform coefficients…”
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On product sets of arithmetic progressions by Max Wenqiang Xu, Yunkun Zhou

“…On product sets of arithmetic progressions, Discrete Analysis 2023:10, 31 pp. The _multiplication table problem_ is a very simply stated question of Erdős: how…”
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Irreducibility of random polynomials of bounded degree by Huy Tuan Pham, Max Wenqiang Xu

“…Irreducibility of random polynomials of bounded degree, Discrete Analysis 2021:7, 16 pp. This paper contributes to a substantial literature on the subject of…”
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Extreme values of Dirichlet polynomials with multiplicative coefficients by Xu, Max Wenqiang, Yang, Daodao

“…We study extreme values of Dirichlet polynomials with multiplicative coefficients, namelyDN(t):=Df,N(t)=1N∑n⩽Nf(n)nit, where f is a completely multiplicative…”
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Better than square-root cancellation for random multiplicative functions by Xu, Max Wenqiang

“…We investigate when the better than square-root cancellation phenomenon exists for ∑ n ≤ N a ( n ) f ( n ) \sum _{n\le N}a(n)f(n) , where a ( n ) ∈ C a(n)\in…”
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On a Turán Conjecture and random multiplicative functions by Angelo, Rodrigo, Xu, Max Wenqiang

“…Abstract We show that if f is the random completely multiplicative function, the probability that $\sum_{n\le x}\frac{f(n)}{n}$ is positive for every x is at…”
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Central limit theorems for random multiplicative functions by Soundararajan, Kannan, Xu, Max Wenqiang

“…A Steinhaus random multiplicative function f is a completely multiplicative function obtained by setting its values on primes f ( p ) to be independent random…”
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Paucity phenomena for polynomial products by Wang, Victor Y., Xu, Max Wenqiang

“…Let P(x)∈Z[x]$P(x)\in \mathbb {Z}[x]$ be a polynomial with at least two distinct complex roots. We prove that the number of solutions…”
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Discrepancy of arithmetic progressions in grids by Fox, Jacob, Xu, Max Wenqiang, Zhou, Yunkun

“…We prove that the discrepancy of arithmetic progressions in the d‐dimensional grid {1,⋯,N}d$\lbrace 1, \dots, N\rbrace ^d$ is within a constant factor…”
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On the random Chowla conjecture by Klurman, Oleksiy, Shkredov, Ilya D., Xu, Max Wenqiang

“…We show that for a Steinhaus random multiplicative function f : N → D and any polynomial P ( x ) ∈ Z [ x ] of deg P ≥ 2 which is not of the form w ( x + c ) d…”
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Multicolor list Ramsey numbers grow exponentially by Fox, Jacob, He, Xiaoyu, Luo, Sammy, Xu, Max Wenqiang

“…The list Ramsey number R ℓ ( H , k ) ${R}_{\ell }(H,k)$, recently introduced by Alon, Bucić, Kalvari, Kuperwasser, and Szabó, is a list‐coloring variant of the…”
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Mixing time of fractional random walk on finite fields by He, Jimmy, Pham, Huy Tuan, Xu, Max Wenqiang

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Better than square-root cancellation for random multiplicative functions by Xu, Max Wenqiang

“…We investigate when the better than square-root cancellation phenomenon exists for $\sum_{n\le N}a(n)f(n)$, where $a(n)\in \mathbb{C}$ and $f(n)$ is a random…”
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Average sizes of mixed character sums by Wang, Victor Y, Xu, Max Wenqiang

“…We prove that the average size of a mixed character sum $$\sum_{1\le n \le x} \chi(n) e(n\theta) w(n/x)$$ (for a suitable smooth function $w$) is on the order…”
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Extreme values of Dirichlet polynomials with multiplicative coefficients by Xu, Max Wenqiang, Yang, Daodao

“…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}…”
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Central limit theorems for random multiplicative functions by Soundararajan, Kannan, Xu, Max Wenqiang

“…A Steinhaus random multiplicative function $f$ is a completely multiplicative function obtained by setting its values on primes $f(p)$ to be independent random…”
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Paucity phenomena for polynomial products by Wang, Victor Y, Xu, Max Wenqiang

“…Bull. Lond. Math. Soc. 56 (2024), no. 8, 2718--2726 Let $P(x)\in \mathbb{Z}[x]$ be a polynomial with at least two distinct complex roots. We prove that the…”
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A polynomial with a root mod $p$ for every $p$ has a real root by Angelo, Rodrigo, Xu, Max Wenqiang

“…We prove that if a polynomial has a root mod $p$ for every large prime $p$, then it has a real root. As an application, we show that the primes can't be…”
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Harper's beyond square-root conjecture by Wang, Victor Y, Xu, Max Wenqiang

“…We explain how the (shifted) Ratios Conjecture for $L(s,\chi)$ would extend a randomization argument of Harper from a conductor-limited range to an unlimited…”
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On a Tur\'an conjecture and random multiplicative functions by Angelo, Rodrigo, Xu, Max Wenqiang

“…We show that if $f$ is the random completely multiplicative function, the probability that $\sum_{n\le x}\frac{f(n)}{n}$ is positive for every $x$ is at least…”
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