Zhi Qi

activity

20142026

most citedOn the Fourier Transform of Bessel Functions over Complex Numbers---I: the Spherical Case

7 citations · 29 across the 30 of their papers we have counts for

collaborators

30 papers

math.NT2026

Hybrid Weyl Subconvexity over Imaginary Quadratic Fields

Zhengxiao Gao, Changlin Li, Zhi Qi

On imaginary quadratic fields, we establish the $GL_{2}$ Bessel $δ$ -method and prove the hybrid Weyl-type subconvexity bound for $GL_{2} \times GL_{1}$ twisted…

math.DS2026

A Criterion for Equidistribution along the $Ω$ Function over Polynomial Sequences with Applications

Zhi Qi, Cheng Zheng

Let $P (Y_{1}, ..., Y_{d})$ be a certain fixed homogeneous polynomial of integral coefficients. In this paper, we establish a quantitative equidistribution criterion for the ergodic av…

math.NT2026

On the Second Moment of $L (1/2, As (f))$

Changlin Li, Zhi Qi

Let $F$ be a real quadratic field. Let $f$ traverse a Hecke orthonormal basis of Hilbert cusp forms over $F$ of full level and parallel weight $(k, k)$ . As $k \…

math.NT2023

Hybrid Weyl-type bound for $p$ -power twisted $GL (2)$ $L$ -functions

Zhengxiao Gao, Shu Luo, Zhi Qi

Let $g$ be a fixed holomorphic cusp form of arbitrary level and nebentypus. Let $χ$ be a primitive character of prime-power modulus $q = p^{γ}$ . In this paper, we prove the following…

math.NT2022

Proof of the Strong Ivić Conjecture for the Cubic Moment of Maass-form $L$ -functions

Zhi Qi

In this paper, we prove the following asymptotic formula for the spectral cubic moment of central $L$ -values: $$ \sum_{t_f \leqslant T} \frac {2 L \big( \tfrac 1 2 , f \big)^3} {L(…

math.NT2022★ 2 cited

Moments of Central $L$ -values for Maass Forms over Imaginary Quadratic Fields

Sheng-Chi Liu, Zhi Qi

In this paper, over imaginary quadratic fields, we consider the family of $L$ -functions $L (s, f)$ for an orthonormal basis of spherical Hecke--Maass forms $f$ with Archimedean par…

math.NT2021

Strong subconvexity for self-dual $GL (3)$ $L$ -functions

Yongxiao Lin, Ramon Nunes, Zhi Qi

In this paper, we prove strong subconvexity bounds for self-dual $GL (3)$ $L$ -functions in the $t$ -aspect and for $GL (3) \times GL (2)$ $L$ -functions in the…

math.NT2021

A Voronoï--Oppenheim summation formula for number fields

Zhi Qi

In this note, we establish a Voronoï--Oppenheim summation formula for divisor functions over an arbitrary number field.

math.NT2021

Beyond the Weyl barrier for $GL (2)$ exponential sums

Roman Holowinsky, Ritabrata Munshi, Zhi Qi

In this paper, we use the Bessel $δ$ -method, along with new variants of the van der Corput method in two dimensions, to prove non-trivial bounds for $GL (2)$ exponential su…

math.NT2020

Bias of Root Numbers for Modular Newforms of Cubic Level

Qinghua Pi, Zhi Qi

Let $H_{2 k}^{\pm} (N^{3})$ denote the set of modular newforms of cubic level $N^{3}$ , weight $2 k$ , and root number $\pm 1$ . For $N > 1$ squarefree and $k > 1$ , we use an analytic method…

math.NT2020★ 1 cited

Subconvexity for $L$ -Functions on $GL_{3}$ over Number Fields

Zhi Qi

In this paper, over an arbitrary number field, we prove subconvexity bounds for self-dual $GL_{3}$ $L$ -functions in the $t$ -aspect and for self-dual $\mathrm{GL}_3 \times \m…

math.NT2019★ 1 cited

Low-lying zeros of $L$ -functions for Maass forms over imaginary quadratic fields

Sheng-Chi Liu, Zhi Qi

We study the $1$ - or $2$ -level density of families of $L$ -functions for Hecke--Maass forms over an imaginary quadratic field $F$ . For test functions whose Fourier transform is supp…

math.NT2019

Cancellation in additively twisted sums on $GL (2)$ with non-linear phase

Yongxiao Lin, Zhi Qi

Let $λ_{g} (n)$ be the Fourier coefficients of a holomorphic cusp modular form $g$ for $SL_{2} (Z)$ . The aim of this article is to get non-trivial bound on non-linear…

math.NT2019

A Bessel delta-method and exponential sums for GL(2)

Keshav Aggarwal, Roman Holowinsky, Yongxiao Lin +1

In this paper, we introduce a simple Bessel $δ$ -method to the theory of exponential sums for $G L_{2}$ . Some results of Jutila on exponential sums are generalized in a less techni…

math.NT2018★ 2 cited

On the Fourier transform of regularized Bessel functions on complex numbers and Beyond Endoscopy over number fields

Zhi Qi

In this article, we prove certain Weber-Schafheitlin type integral formulae for Bessel functions over complex numbers. A special case is a formula for the Fourier transform of regu…

math.RT2018★ 1 cited

On the Waldspurger Formula and the Metaplectic Ramanujan Conjecture over Number Fields

Jingsong Chai, Zhi Qi

In this paper, by inputting the Bessel identities over the complex field in previous work of the authors, the Waldspurger formula of Baruch and Mao is extended from totally real fi…

math.RT2018

A Whittaker-Plancherel Inversion Formula for $SL_{2} (C)$

Zhi Qi, Chang Yang

In this paper, we establish a Whittaker-Plancherel inversion formula for $SL_{2} (C)$ from the analytic perspective of the Bessel transform of Bruggeman and Motohash…

math.NT2018★ 1 cited

Subconvexity for twisted $L$ -functions on $GL_{3}$ over the Gaussian number field

Zhi Qi

Let $q \in Z [i]$ be prime and $χ$ be the primitive quadratic Hecke character modulo $q$ . Let $π$ be a self-dual Hecke automorphic cusp form for $\mathrm{SL}_3 (\mathbb{Z}…

math.RT2018★ 1 cited

Bessel Identities in the Waldspurger Correspondence over the Complex Numbers

Jingsong Chai, Zhi Qi

We prove certain identities between relative Bessel functions attached to irreducible unitary representations of $PGL_{2} (C)$ and Bessel functions attached to irred…

math.CA2016★ 5 cited

Theory of Fundamental Bessel Functions of High Rank

Zhi Qi

In this article, we shall study fundamental Bessel functions for $GL_{n} (F)$ arising from the Voronoï summation formula for any rank $n$ and field $\mathbb{F} = \ma…

math.NT2016★ 2 cited

Cancellation in the Additive Twists of Fourier Coefficients for $GL_{2}$ and $GL_{3}$ over Number Fields

Zhi Qi

In this article, we study the sum of additively twisted Fourier coefficients of an irreducible cuspidal automorphic representation of $GL_{2}$ or $GL_{3}$ over an arb…

math.CA2016

On the Fourier Transform of Bessel Functions over Complex Numbers---II: the General Case

Zhi Qi

In this paper, we prove an exponential integral formula for the Fourier transform of Bessel functions over complex numbers, along with a radial exponential integral formula. The fo…

math.CA2016★ 7 cited

On the Fourier Transform of Bessel Functions over Complex Numbers---I: the Spherical Case

Zhi Qi

In this note, we shall prove a formula for the Fourier transform of spherical Bessel functions over complex numbers, viewed as the complex analogue of the classical formulae of Har…

math.RT2016

On the Kuznetsov Trace Formula for $PGL_{2} (C)$

Zhi Qi

In this note, using a representation theoretic method of Cogdell and Piatetski-Shapiro, we prove the Kuznetsov trace formula for an arbitrary discrete group $Γ$ in $\mathrm{PGL}_2(…

Hybrid Weyl Subconvexity over Imaginary Quadratic Fields

A Criterion for Equidistribution along the Ω Function over Polynomial Sequences with Applications

On the Second Moment of L(1/2,As(f))

Hybrid Weyl-type bound for p-power twisted GL(2) L-functions

Proof of the Strong Ivić Conjecture for the Cubic Moment of Maass-form L-functions

Moments of Central L-values for Maass Forms over Imaginary Quadratic Fields

Strong subconvexity for self-dual GL(3) L-functions

A Voronoï--Oppenheim summation formula for number fields

Beyond the Weyl barrier for GL(2) exponential sums

Bias of Root Numbers for Modular Newforms of Cubic Level

Subconvexity for L-Functions on GL3​ over Number Fields

Low-lying zeros of L-functions for Maass forms over imaginary quadratic fields

Cancellation in additively twisted sums on GL(2) with non-linear phase

A Bessel delta-method and exponential sums for GL(2)

On the Fourier transform of regularized Bessel functions on complex numbers and Beyond Endoscopy over number fields

On the Waldspurger Formula and the Metaplectic Ramanujan Conjecture over Number Fields

A Whittaker-Plancherel Inversion Formula for SL2​(C)

Subconvexity for twisted L-functions on GL3​ over the Gaussian number field

Bessel Identities in the Waldspurger Correspondence over the Complex Numbers

Theory of Fundamental Bessel Functions of High Rank

Cancellation in the Additive Twists of Fourier Coefficients for GL2​ and GL3​ over Number Fields

On the Fourier Transform of Bessel Functions over Complex Numbers---II: the General Case

On the Fourier Transform of Bessel Functions over Complex Numbers---I: the Spherical Case

On the Kuznetsov Trace Formula for PGL2​(C)

A Criterion for Equidistribution along the $Ω$ Function over Polynomial Sequences with Applications

On the Second Moment of $L (1/2, As (f))$

Hybrid Weyl-type bound for $p$ -power twisted $GL (2)$ $L$ -functions

Proof of the Strong Ivić Conjecture for the Cubic Moment of Maass-form $L$ -functions

Moments of Central $L$ -values for Maass Forms over Imaginary Quadratic Fields

Strong subconvexity for self-dual $GL (3)$ $L$ -functions

Beyond the Weyl barrier for $GL (2)$ exponential sums

Subconvexity for $L$ -Functions on $GL_{3}$ over Number Fields

Low-lying zeros of $L$ -functions for Maass forms over imaginary quadratic fields

Cancellation in additively twisted sums on $GL (2)$ with non-linear phase

A Whittaker-Plancherel Inversion Formula for $SL_{2} (C)$

Subconvexity for twisted $L$ -functions on $GL_{3}$ over the Gaussian number field

Cancellation in the Additive Twists of Fourier Coefficients for $GL_{2}$ and $GL_{3}$ over Number Fields

On the Kuznetsov Trace Formula for $PGL_{2} (C)$