5 citations · 14 across the 13 of their papers we have counts for
14 papers
A weighted formulation of refined decoupling and inequalities of Mizohata-Takeuchi-type for the moment curve
Anthony Carbery, Zane Kun Li, Yixuan Pang +1
Let be a compact patch of a well-curved curve in with induced Lebesgue measure , and let be the Fourier e…
An improved example for an autoconvolution inequality
Christopher Boyer, Zane Kun Li
We give a nonnegative step function with 575 equally spaced intervals such that $$\frac{\|f \ast f\|_{L^{2}(\mathbb{R})}^{2}}{\|f \ast f\|_{L^{\infty}(\mathbb{R})}\|f \ast f\|_{L^{…
Strichartz inequalities: some recent developments
Jianhui Li, Zane Kun Li, Po-Lam Yung
Strichartz inequalities, originating from Fourier restriction theory, play a central role in the analysis of dispersive partial differential equations. They serve as a cornerstone…
Mixed norm decoupling for paraboloids
Shival Dasu, Hongki Jung, Zane Kun Li +1
We prove the sharp mixed norm decoupling estimate for the paraboloid in dimensions.
An introduction to decoupling and harmonic analysis over
Zane Kun Li
The goal of this expository paper is to provide an introduction to decoupling by working in the simpler setting of decoupling for the parabola over . Over $\mathbb{Q}…
A decoupling interpretation of an old argument for Vinogradov's Mean Value Theorem
Brian Cook, Kevin Hughes, Zane Kun Li +3
We interpret into decoupling language a refinement of a 1973 argument due to Karatsuba on Vinogradov's mean value theorem. The main goal of our argument is to answer what precisely…
Improved discrete restriction for the parabola
Shaoming Guo, Zane Kun Li, Po-Lam Yung
Using ideas from Guth-Maldague-Wang and working over , we show that the discrete restriction constant for the parabola is $O_{\varepsilon}((\log M)^{2 + \varepsilon})…
Decoupling for fractal subsets of the parabola
Alan Chang, Jaume de Dios Pont, Rachel Greenfeld +3
We consider decoupling for a fractal subset of the parabola. We reduce studying decoupling for a fractal subset on the parabola to stu…
A bilinear proof of decoupling for the cubic moment curve
Shaoming Guo, Zane Kun Li, Po-Lam Yung
Using a bilinear method that is inspired by the method of efficient congruencing of Wooley [Woo16], we prove a sharp decoupling inequality for the moment curve in .
An decoupling interpretation of efficient congruencing: the parabola
Zane Kun Li
We give a new proof of decoupling for the parabola inspired from efficient congruencing. Making quantitative this proof matches a bound obtained by Bourgain for the discrete…
Effective decoupling for the parabola
Zane Kun Li
We make effective decoupling for the parabola in the range . In an appendix joint with Jean Bourgain, we apply the main theorem to prove the conjectural bound…
Quadratic Twists of Elliptic Curves with 3-Selmer Rank 1
Zane Kun Li
A weaker form of a 1979 conjecture of Goldfeld states that for every elliptic curve , a positive proportion of its quadratic twists have rank 1. Using tools…
Arithmetic Properties of Picard-Fuchs Equations and Holonomic Recurrences
Zane Kun Li, Alexander W. Walker
The coefficient series of the holomorphic Picard-Fuchs differential equation associated with the periods of elliptic curves often have surprising number-theoretic properties. These…
Elliptic Curves with Full 2-Torsion and Maximal Adelic Galois Representations
David Corwin, Tony Feng, Zane Kun Li +1
In 1972, Serre showed that the adelic Galois representation associated to a non-CM elliptic curve over a number field has open image in GL_2(\hat{Z}). In Greicius' thesis, he devel…