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Qingfeng Sun

Publications and source records attributed to Qingfeng Sun.

51 records · Page 3Linked to original sources
arXiv2020

A subconvex bound for twisted $L$-functions

Let $\mathfrak{q}>2$ be a prime number, $χ$ a primitive Dirichlet character modulo $\mathfrak{q}$ and $f$ a primitive holomorphic cusp form or a Hecke-Maass cusp form of level $\mathfrak{q}$ and trivial nebentypus. We prove the subconvex bound $$ L(1/2,f\otimes χ)\ll \mathfrak{q}^{1/2-1/12+\varepsilon}, $$ where the implicit constant depends only on the archimedean parameter of $f$ and $\varepsilon$. The main input is a modifying trivial delta method developed in [1].

math.NT↗
arXiv2020

The Burgess bound via a trivial delta method

Let $g$ be a fixed Hecke cusp form for $\mathrm{SL}(2,\mathbb{Z})$ and $χ$ be a primitive Dirichlet character of conductor $M$. The best known subconvex bound for $L(1/2,g\otimes χ)$ is of Burgess strength. The bound was proved by a couple of methods: shifted convolution sums and the Petersson/Kuznetsov formula analysis. It is natural to ask what inputs are really needed to prove a Burgess-type bound on $\rm GL(2)$. In this paper, we give a new proof of the Burgess-type bounds ${L(1/2,g\otimes χ)\ll_{g,\varepsilon} M^{1/2-1/8+\varepsilon}}$ and $L(1/2,χ)\ll_{\varepsilon} M^{1/4-1/16+\varepsilon}$ that does not require the basic tools of the previous proofs and instead uses a trivial delta method.

math.NT↗
arXiv2018

Bounds for $GL_3$ $L$-functions in depth aspect

Let $f$ be a Hecke-Maass cusp form for $SL_3(\mathbb{Z})$ and $χ$ a primitive Dirichlet character of prime power conductor $\mathfrak{q}=p^κ$ with $p$ prime and $κ\geq 10$. We prove a subconvexity bound $$ L\left(\frac{1}{2},π\otimes χ\right)\ll_{p,π,\varepsilon} \mathfrak{q}^{3/4-3/40+\varepsilon} $$ for any $\varepsilon>0$, where the dependence of the implied constant on $p$ is explicit and polynomial. We obtain this result by applying the circle method of Kloosterman's version, summation formulas of Poisson and Voronoi's type and a conductor lowering mechanism introduced by Munshi [14]. The main new technical estimates are the essentially square root bounds for some twisted multi-dimensional character sums, which are proved by an elementary method.

math.NT↗
arXiv2017

Hybrid bounds for twists of $GL(3)$ $L$-functions

Let $π$ be a Hecke-Maass cusp form for $SL(3,\mathbb{Z})$ and $χ=χ_1χ_2$ a Dirichlet character with $χ_i$ primitive modulo $M_i$. Suppose that $M_1$, $M_2$ are primes such that $\max\{(M|t|)^{1/3+2δ/3},M^{2/5}|t|^{-9/20}, M^{1/2+2δ}|t|^{-3/4+2δ}\}(M|t|)^{\varepsilon} 0$, where $M=M_1M_2$, $|t|\geq 1$ and $0<δ< 1/52$. Then we have $$ L\left(\frac{1}{2}+it,π\otimes χ\right)\ll_{π,\varepsilon} (M|t|)^{3/4-δ+\varepsilon}. $$

math.NT↗
arXiv2017

Shifted convolution sums involving theta series

Let $f$ be a cuspidal newform (holomorphic or Maass) of arbitrary level and nebentypus and denote by $λ_f(n)$ its $n$-th Hecke eigenvalue. Let $$ r(n)=\#\left\{(n_1,n_2)\in \mathbb{Z}^2:n_1^2+n_2^2=n\right\}. $$ In this paper, we study the shifted convolution sum $$ \mathcal{S}_h(X)=\sum_{n\leq X}λ_f(n+h)r(n), \qquad 1\leq h\leq X, $$ and establish uniform bounds with respect to the shift $h$ for $\mathcal{S}_h(X)$.

math.NT↗
arXiv2017

Averages of shifted convolution sums for $GL(3) \times GL(2)$

Let $A_f(1,n)$ be the normalized Fourier coefficients of a $GL(3)$ Maass cusp form $f$ and let $a_g(n)$ be the normalized Fourier coefficients of a $GL(2)$ cusp form $g$. Let $λ(n)$ be either $A_f(1,n)$ or the triple divisor function $d_3(n)$. It is proved that for any $ε>0$, any integer $r\geq 1$ and $r^{5/2}X^{1/4+7δ/2}\leq H\leq X$ with $δ>0$, $$ \frac{1}{H}\sum_{h\geq 1}W\left(\frac{h}{H}\right) \sum_{n\geq 1}λ(n)a_g(rn+h)V\left(\frac{n}{X}\right)\ll X^{1-δ+ε}, $$ where $V$ and $W$ are smooth compactly supported functions, and the implied constants depend only on the associated forms and $ε$.

math.NT↗
arXiv2016

Shifted convolution sums of $GL_3$ cusp forms with $θ$-series

Let $A_f(1,n)$ be the normalized Fourier coefficients of a Hecke-Maass cusp form $f$ for $SL_3(\mathbb{Z})$ and $$ r_3(n)=\#\left\{(n_1,n_2,n_3)\in \mathbb{Z}^3:n_1^2+n_2^2+n_3^2=n\right\}. $$ Let $1\leq h\leq X$ and $ϕ(x)$ be a smooth function compactly supported on $[1/2,1]$. It is shown that $$ \sum_{n\geq 1}A_f(1,n+h)r_3(n)ϕ\left(\frac{n}{X}\right) \ll_{f,\varepsilon} X^{\frac{3}{2}-\frac{1}{8}+\varepsilon} $$ uniformly with respect to the shift $h$.

math.NT↗
arXiv2016

A note on simultaneous nonvanishing of Dirichlet $L$-functions and twists of Hecke-Maass $L$-functions

In this note, we prove that given a Hecke-Maass cusp form $f$ for $SL_2(\mathbb{Z})$ and a sufficiently large integer $q=q_1q_2$ with $q_j\asymp \sqrt{q}$ being prime numbers for $j=1,2$, there exists a primitive Dirichlet character $χ$ of conductor $q$ such that $L\left(\frac{1}{2},f\otimes χ\right)L\left(\frac{1}{2},χ\right)\neq 0$. To prove this, we establish asymptotic formulas of $L\left(\frac{1}{2},f\otimes χ\right)L\left(\frac{1}{2},χ\right)$ over the family of even primitive Dirichlet characters $χ$ of conductor $q$ for more general $q$.

math.NT↗
arXiv2016

Majorana fermions in a superconducting Mobius strip

Recently, much attention has been paid to search for Majorana fermions in solid-state systems. Among various proposals there is one based on radio-frequency superconducting quantum interference devices (rf-SQUIDs), in which the appearance of 4$π$-period energy-phase relations is regarded as smoking-gun evidence of Majorana fermion states. Here we report the observation of truncated 4$π$-period (i.e., 2$π$-period but fully skewed) oscillatory patterns of contact resistance on rf-SQUIDs constructed on the surface of three-dimensional topological insulator Bi$_2$Te$_3$. The results reveal the existence of 1/2 fractional modes of Cooper pairs and the occurrence of parity switchings, both of which are necessary signatures accompanied with the formation of Majorana fermion states.

cond-mat.mes-hall↗
arXiv2015

Sums of the triple divisor function over values of a ternary quadratic form

Let $τ_3(n)$ be the triple divisor function which is the number of solutions of the equation $d_1d_2d_3=n$ in natural numbers. It is shown that $$ \sum_{1\leq n_1,n_2,n_3\leq \sqrt{x}}τ_3(n_1^2+n_2^2+n_3^2)=c_1x^{\frac{3}{2}}(\log x)^2+ c_2x^{\frac{3}{2}}\log x +c_3x^{\frac{3}{2}} +O_{\varepsilon}(x^{\frac{11}{8}+\varepsilon}) $$ for some constants $c_1$, $c_2$ and $c_3$.

math.NT↗
arXiv2014

Transport discovery of emerging robust helical surface states in $Z_2=0$ systems

We study the possibility of realizing robust helical surface states in $Z_2=0$ systems. We find that the combination of anisotropy and finite-size confinement leads to the emergence of robust helical edge states in both 2D and 3D $Z_2=0$ systems. By investigating an anisotropic Bernevig-Hughes-Zhang model in a finite sample, we demonstrate that the transport manifestation of the surface states is robust against non-magnetic disorder, resembling that of a $Z_2 = 1$ phase. Notably, the effective energy gap for the robust helical states can be efficiently engineered, allowing for potential applications as valley filters and valley valves. The realization of emerging robust helical surface states in realistic material is also discussed.

cond-mat.mes-hall↗
arXiv2012

Shot noise of spin current and spin transfer torque

We report the theoretical investigation of noise spectrum of spin current and spin transfer torque for non-colinear spin polarized transport in a spin-valve device which consists of normal scattering region connected by two ferromagnetic electrodes. Our theory was developed using non-equilibrium Green's function method and general non-linear $S^σ-V$ and $S^τ-V$ relations were derived as a function of angle $θ$ between magnetization of two leads. We have applied our theory to a quantum dot system with a resonant level coupled with two ferromagnetic electrodes. It was found that for the MNM system, the auto-correlation of spin current is enough to characterize the fluctuation of spin current. For a system with three ferromagnetic layers, however, both auto-correlation and cross-correlation of spin current are needed to characterize the noise spectrum of spin current. Furthermore, the spin transfer torque and the torque noise were studied for the MNM system. For a quantum dot with a resonant level, the derivative of spin torque with respect to bias voltage is proportional to $\sinθ$ when the system is far away from the resonance. When the system is near the resonance, the spin transfer torque becomes non-sinusoidal function of $θ$. The derivative of noise spectrum of spin transfer torque with respect to the bias voltage $N_τ$ behaves differently when the system is near or far away from the resonance. Specifically, the differential shot noise of spin transfer torque $N_τ$ is a concave function of $θ$ near the resonance while it becomes convex function of $θ$ far away from resonance. For certain bias voltages, the period $N_τ(θ)$ becomes $π$ instead of $2π$. For small $θ$, it was found that the differential shot noise of spin transfer torque is very sensitive to the bias voltage and the other system parameters.

cond-mat.mes-hall↗
arXiv2006

Universal spin-Hall conductance fluctuations in two dimensions

We report a theoretical investigation on spin-Hall conductance fluctuation of disordered four terminal devices in the presence of Rashba or/and Dresselhaus spin-orbital interactions in two dimensions. As a function of disorder, the spin-Hall conductance $G_{sH}$ shows ballistic, diffusive and insulating transport regimes. For given spin-orbit interactions, a universal spin-Hall conductance fluctuation (USCF) is found in the diffusive regime. The value of the USCF depends on the spin-orbit coupling $t_{so}$, but is independent of other system parameters. It is also independent of whether Rashba or Dresselhaus or both spin-orbital interactions are present. When $t_{so}$ is comparable to the hopping energy $t$, the USCF is a universal number $\sim 0.18 e/4π$. The distribution of $G_{sH}$ crosses over from a Gaussian distribution in the metallic regime to a non-Gaussian distribution in the insulating regime as the disorder strength is increased.

cond-mat.mes-hall↗
arXiv2005

Detection of Single Electron Charging in an Individual InAs Quantum Dot by Noncontact Atomic Force Microscopy

Single electron charging in an individual InAs quantum dot was observed by electrostatic force measurements with an atomic force microscope (AFM). The resonant frequency shift and the dissipated energy of an oscillating AFM cantilever were measured as a function of the tip-back electrode voltage and the resulting spectra show distinct jumps when the tip was positioned above the dot. The observed jumps in the frequency shift, with corresponding peaks in dissipation, are attributed to a single electron tunneling between the dot and the back electrode governed by Coulomb blockade effect, and are consistent with a model based on the free energy of the system. The observed phenomenon may be regarded as the ``force version'' of the Coulomb blockade effect.

cond-mat.mtrl-sci↗
arXiv2002

Parametric quantum spin pump

We investigate a non-adiabatic parametric quantum pump consists of a nonmagnetic scattering region connected by two ferromagnetic leads. The presence of ferromagnetic leads allows electrons with different spins to experience different potential landscape. Using this effect we propose a quantum spin pump that drives spin-up electrons to flow in one direction and spin-down electrons to flow in opposite direction. As a result, the spin pump can deliver a spin current with vanishing charge current.

cond-mat↗