Zobrazeno 1 - 10
of 604
pro vyhledávání: '"Wang, Victor"'
Autor:
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 of $\sqrt{x}$ for all irrational real $\theta$ satisfying a weak Diophantine condition, whe
Externí odkaz:
http://arxiv.org/abs/2411.14181
We prove upper and lower bounds on the number of pairs of commuting $n\times n$ matrices with integer entries in $[-T,T]$, as $T\to \infty$. Our work uses Fourier analysis and leads us to an analysis of exponential sums involving matrices over finite
Externí odkaz:
http://arxiv.org/abs/2409.01920
We use the circle method to prove that a density 1 of elements in $\mathbb{F}_q[t]$ are representable as a sum of three cubes of essentially minimal degree from $\mathbb{F}_q[t]$, assuming the Ratios Conjecture and that the characteristic is bigger t
Externí odkaz:
http://arxiv.org/abs/2408.03668
We count integral quaternion zeros of $\gamma_1^2 \pm \dots \pm \gamma_n^2$, giving an asymptotic when $n\ge 9$, and a likely near-optimal bound when $n=8$. To do so, we introduce a new, nonabelian delta symbol method, which is of independent interes
Externí odkaz:
http://arxiv.org/abs/2407.11804
Autor:
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 range of ``beyond square-root cancellation'' for character twists of the Liouville function.
Externí odkaz:
http://arxiv.org/abs/2405.04094
We use a function field version of the circle method to prove that a positive proportion of elements in $\mathbb{F}_q[t]$ are representable as a sum of three cubes of minimal degree from $\mathbb{F}_q[t]$, assuming a suitable form of the Ratios Conje
Externí odkaz:
http://arxiv.org/abs/2402.07146
Autor:
Wang, Victor Y.
This semi-expository note clarifies the extent to which recent ideas in homological stability can resolve the Ratios Conjecture over $\mathbb{F}_q(t)$. For large fixed $q$, a uniform power saving at distance $\ge q^{-\delta}$ from the critical line i
Externí odkaz:
http://arxiv.org/abs/2402.01214
Autor:
Wang, Victor Y.
By studying some Clausen-like multiple Dirichlet series, we complete the proof of Manin's conjecture for sufficiently split smooth equivariant compactifications of the translation-dilation group over the rationals. Secondary terms remain elusive in g
Externí odkaz:
http://arxiv.org/abs/2309.07626
Autor:
Ueda, Hiroki, Mankowsky, Roman, Paris, Eugenio, Sander, Mathias, Deng, Yunpei, Liu, Biaolong, Leroy, Ludmila, Nag, Abhishek, Skoropata, Elizabeth, Ukleev, Chennan Wang Victor, Perren, Gérard Sylvester, Dössegger, Janine, Gurung, Sabina, Abreu, Elsa, Savoini, Matteo, Kimura, Tsuyoshi, Patthey, Luc, Razzoli, Elia, Lemke, Henrik Till, Johnson, Steven Lee, Staub, Urs
Interactions between the different degrees of freedom form the basis of many manifestations of intriguing physics in condensed matter. In this respect, quantifying the dynamics of normal modes that themselves arise from these interactions and how the
Externí odkaz:
http://arxiv.org/abs/2306.02676