Bingrong Huang

activity

20142023

most citedOn the Rankin--Selberg problem

72 citations · 157 across the 24 of their papers we have counts for

collaborators

24 papers

math.NT2023

On the Rankin--Selberg problem, II

Bingrong Huang

In this paper, we improve our bounds on the Rankin--Selberg problem. That is, we obtain smaller error term of the second moment of Fourier coefficients of a $GL (2)$ cusp form (…

math.NT2022★ 2 cited

Extreme central $L$ -values of almost prime quadratic twists of elliptic curves

Shenghao Hua, Bingrong Huang

In this paper, we prove the extreme values of $L$ -functions at the central point for almost prime quadratic twists of an elliptic curve. As an application, we get the extreme value…

math.NT2022★ 3 cited

The cubic moment of Hecke--Maass cusp forms and moments of $L$ -functions

Bingrong Huang

In this paper, we prove the smooth cubic moments vanish for the Hecke--Maass cusp forms, which gives a new case of the random wave conjecture. In fact, we can prove a polynomial de…

math.NT2022★ 3 cited

Effective decorrelation of Hecke eigenforms

Bingrong Huang

In this paper, we prove effective quantitative decorrelation of values of two Hecke eigenforms as the weight goes to infinity. As consequences, we get an effective version of equid…

math.NT2022★ 1 cited

Lower bounds for moments of quadratic twisted self-dual $GL (3)$ central $L$ -values

Shenghao Hua, Bingrong Huang

In this paper, we prove the conjectured order lower bound for the $k$ -th moment of central values of quadratic twisted self-dual $GL (3)$ $L$ -functions for all $k \geq 1$ , b…

math.NT2021

Analytic twists of $G L_{2} \times G L_{2}$ automorphic forms

Bingrong Huang, Qingfeng Sun, Huimin Zhang

Let $f$ and $g$ be holomorphic or Maass cusp forms for $S L_{2} (Z)$ with normalized Fourier coefficients $λ_{f} (n)$ and $λ_{g} (n)$ , respectively. In this paper, we prove nont…

math.NT2021★ 2 cited

Uniform bounds for $GL (3) \times GL (2)$ $L$ -functions

Bingrong Huang

In this paper, we prove uniform bounds for $GL (3) \times GL (2)$ $L$ -functions in the $GL (2)$ spectral aspect and the $t$ aspect by a delta method. More precisely, let $ϕ$ b…

math.NT2021★ 6 cited

Hybrid subconvexity bounds for twists of $GL (3) \times GL (2)$ $L$ -functions

Bingrong Huang, Zhao Xu

In this paper, we solve the hybrid subconvexity problem for $GL (3) \times GL (2)$ $L$ -functions twisted by a primtive Dirichlet charater modulo $M$ (prime) in the $M$ - and $t$ -…

math.NT2020

Quantum variance for dihedral Maass forms

Bingrong Huang, Stephen Lester

We establish an asymptotic formula for the weighted quantum variance of dihedral Maass forms on $Γ_{0} (D) \ H$ in the large eigenvalue limit, for certain fixed $D$ .…

math.NT2020

Averages of coefficients of a class of degree 3 L-functions

Bingrong Huang, Yongxiao Lin, Zhiwei Wang

In this note, we give a detailed proof of an asymptotic for averages of coefficients of a class of degree three $L$ -functions which can be factorized as a product of a degree one a…

math.NT2020★ 72 cited

On the Rankin--Selberg problem

Bingrong Huang

In this paper, we solve the Rankin--Selberg problem. That is, we break the well known Rankin--Selberg's bound on the error term of the second moment of Fourier coefficients of a $\…

math.NT2019★ 29 cited

Analytic twists of $G L_{3} \times G L_{2}$ automorphic forms

Yongxiao Lin, Qingfeng Sun

Let $π$ be a Hecke--Maass cusp form for $S L_{3} (Z)$ with normalized Hecke eigenvalues $λ_{π} (n, r)$ . Let $f$ be a holomorphic or Maass cusp form for $S L_{2} (Z)$ …

math.NT2019

Gaussian primes in almost all narrow sectors

Bingrong Huang, Jianya Liu, Zeév Rudnick

We study Gaussian primes lying in narrow sectors, and show that almost all such sectors contain the expected number of primes, if the sectors are not too narrow.

math.NT2018

Quantum variance for Eisenstein Series

Bingrong Huang

In this paper, we prove an asymptotic formula for the quantum variance for Eisenstein series on $PSL_{2} (Z) \ H$ . The resulting quadratic form is c…

math.NT2018

Effective joint equidistribution of primitive rational points on expanding horospheres

Daniel El-Baz, Bingrong Huang, Min Lee

We prove an effective version of a result due to Einsiedler, Mozes, Shah and Shapira who established the equidistribution of primitive rational points on expanding horospheres in t…

math.NT2018★ 1 cited

Non-vanishing of Maass form L-functions at the critical point

Olga Balkanova, Bingrong Huang, Anders Södergren

In this paper, we consider the family ${L_{j} (s)}_{j = 1}^{\infty}$ of $L$ -functions associated to an orthonormal basis ${u_{j}}_{j = 1}^{\infty}$ of even Hecke-Maass forms for the mod…

math.DS2018★ 1 cited

Uniform distribution of saddle connection lengths

Jon Chaika, Donald Robertson

For almost every flat surface the sequence of saddle connection lengths listed in increasing order is uniformly distributed mod one.

math.NT2018

Super-positivity of a family of L-functions in the level aspect

Dorian Goldfeld, Bingrong Huang

An automorphic self dual L-function has the super-positivity property if all derivatives of the completed L-function at the central point $s = 1/2$ are non-negative and all derivativ…

math.NT2018

Prime lattice points in ovals

Bingrong Huang, Zeév Rudnick

We study the distribution of lattice points with prime coordinates lying in the dilate of a convex planar domain having smooth boundary, with nowhere vanishing curvature. Counting…

math.NT2017

Mollification and non-vanishing of automorphic $L$ -functions on GL(3)

Bingrong Huang, Shenhui Liu, Zhao Xu

We prove a non-vanishing result for central values of $L$ -functions on GL(3), by using the mollification method and the Kuznetsov trace formula.

math.NT2016★ 3 cited

Super-positivity of a family of L-functions

Dorian Goldfeld, Bingrong Huang

Zhiwei Yun and Wei Zhang introduced the notion of "super-positivity of self dual L-functions" which specifies that all derivatives of the completed L-function (including Gamma fact…

math.NT2015★ 9 cited

Sup-norm bounds for Eisenstein series

Bingrong Huang, Zhao Xu

The paper deals with establishing bounds for Eisenstein series on congruence quotients of the upper half plane, with control of both the spectral parameter and the level. The key o…

math.NT2014★ 19 cited

Exponential sums over primes in short intervals and an application to the Waring--Goldbach problem

Bingrong Huang

Let $Λ (n)$ be the von Mangoldt function, $x$ real and $2 \leq y \leq x$ . This paper improves the estimate on the exponential sum over primes in short intervals \[ S_k(x,y;α) = \sum_…

math.NT2014★ 6 cited

Strong orthogonality between the Mobius function and nonlinear exponential functions in short intervals

Bingrong Huang

Let $μ (n)$ be the Möbius function, $e (z) = exp (2 π i z)$ , $x$ real and $2 \leq y \leq x$ . This paper proves two sequences $(μ (n))$ and $(e (n^{k} α))$ are strongly orthogonal in short in…

On the Rankin--Selberg problem, II

Extreme central L-values of almost prime quadratic twists of elliptic curves

The cubic moment of Hecke--Maass cusp forms and moments of L-functions

Effective decorrelation of Hecke eigenforms

Lower bounds for moments of quadratic twisted self-dual GL(3) central L-values

Analytic twists of GL2​×GL2​ automorphic forms

Uniform bounds for GL(3)×GL(2) L-functions

Hybrid subconvexity bounds for twists of GL(3)×GL(2) L-functions

Quantum variance for dihedral Maass forms

Averages of coefficients of a class of degree 3 L-functions

On the Rankin--Selberg problem

Analytic twists of GL3​×GL2​ automorphic forms

Gaussian primes in almost all narrow sectors

Quantum variance for Eisenstein Series

Effective joint equidistribution of primitive rational points on expanding horospheres

Non-vanishing of Maass form L-functions at the critical point

Uniform distribution of saddle connection lengths

Super-positivity of a family of L-functions in the level aspect

Prime lattice points in ovals

Mollification and non-vanishing of automorphic L-functions on GL(3)

Super-positivity of a family of L-functions

Sup-norm bounds for Eisenstein series

Exponential sums over primes in short intervals and an application to the Waring--Goldbach problem

Strong orthogonality between the Mobius function and nonlinear exponential functions in short intervals

Extreme central $L$ -values of almost prime quadratic twists of elliptic curves

The cubic moment of Hecke--Maass cusp forms and moments of $L$ -functions

Lower bounds for moments of quadratic twisted self-dual $GL (3)$ central $L$ -values

Analytic twists of $G L_{2} \times G L_{2}$ automorphic forms

Uniform bounds for $GL (3) \times GL (2)$ $L$ -functions

Hybrid subconvexity bounds for twists of $GL (3) \times GL (2)$ $L$ -functions

Analytic twists of $G L_{3} \times G L_{2}$ automorphic forms

Mollification and non-vanishing of automorphic $L$ -functions on GL(3)