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5 papers
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})…
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…
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…