2 citations · 4 across the 12 of their papers we have counts for
13 papers
PageRank on Lubotzky--Phillips--Sarnak graphs
Shenghao Hua
We compare return probabilities for random walks stopped at an independent geometric time on Lubotzky--Phillips--Sarnak graphs and on the infinite regular tree, with the McKay meas…
Prime pairs along rays of prime indices
Shenghao Hua, Sizhe Xie
Let be the prime with index . We prove that the ratios for which is a square are dense in . The same is true when is a square.…
Universal murmuration and Hecke augmentation
Shenghao Hua, Chung Pang Mok
Prime coefficients of elliptic curves exhibit murmurations, statistical patterns that support the prediction of arithmetic labels. We conjecture that root number weighted averages…
Decorrelation of Bessel periods for symmetric cubes of
Shenghao Hua, Xinchen Miao
We demonstrate that for symmetric cubes of algebraic regular Hecke eigenforms on , a decorrelation phenomenon occurs for global Bessel periods of $\mathrm{SO}(5)\ti…
Selberg orthogonality for half-integral weight modular forms
Shenghao Hua
The Keating--Snaith conjecture for orthogonal families may be viewed as analogous to a Gaussian distribution with a negative mean, and the possibility that mixed moments resemble a…
An evident corollary arising from Newton-Thorne
Shenghao Hua
Let be a primitive holomorphic newform of weight at least and arbitrary level. We consider the representations obtained from its symmetric powers by taking tensor products,…
Discrete restrictions from Laurent monomial systems for multiple Dirichlet series
Shenghao Hua
We introduce a special class of multiple Dirichlet series whose terms are supported on a variety and which admit an Euler product structure.
Quadratic forms of modular forms
Shenghao Hua
In this paper, we study quadratic forms in spaces of holomorphic cusp forms. We show, conditionally, that when two quadratic forms in Hecke eigenforms share no common diagonal term…
-derivatives of the fixed elliptic curve over rank-one imaginary quadratic fields
Shenghao Hua
There is a one-sided central limit theorem for the logarithms of -derivatives of a fixed rational non-CM elliptic curve over imaginary quadratic fields of rank one, analogou…
Joint value distribution of Hecke--Maass forms
Shenghao Hua, Bingrong Huang, Liangxun Li
In this paper, we formulate a conjecture on joint distribution of Hecke--Maass cusp forms. To support our conjecture, we prove two conditional results on joint moments of two Hecke…
Extreme central values of quadratic Dirichlet -functions with prime conductors
Mingyue Fan, Shenghao Hua, Sizhe Xie
In this paper we prove a lower bound result for extremely large values of with prime numbers .
Extreme central -values of almost prime quadratic twists of elliptic curves
Shenghao Hua, Bingrong Huang
In this paper, we prove the extreme values of -functions at the central point for almost prime quadratic twists of an elliptic curve. As an application, we get the extreme value…
Lower bounds for moments of quadratic twisted self-dual central -values
Shenghao Hua, Bingrong Huang
In this paper, we prove the conjectured order lower bound for the -th moment of central values of quadratic twisted self-dual -functions for all , b…