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Jia-Wei Guo

Publications and source records attributed to Jia-Wei Guo.

11 recordsLinked to original sources
arXiv2026

Hurwitz class number relations and mock modular forms

A classical class number relation of Hurwitz expresses the Fourier coefficients of the product of a unary theta function and the class number generating function. Here, we establish an infinite family of analogous class number relations obtained by replacing the unary quadratic form $m^2$ by positive-definite binary quadratic forms. These identities involve Cohen's generalized class numbers and depend only on the genus of the underlying quadratic form. For this, we construct a genus-dependent level-lowering operator.

math.NT↗
arXiv2023

Sparse Depth-Guided Attention for Accurate Depth Completion: A Stereo-Assisted Monitored Distillation Approach

This paper proposes a novel method for depth completion, which leverages multi-view improved monitored distillation to generate more precise depth maps. Our approach builds upon the state-of-the-art ensemble distillation method, in which we introduce a stereo-based model as a teacher model to improve the accuracy of the student model for depth completion. By minimizing the reconstruction error of a target image during ensemble distillation, we can avoid learning inherent error modes of completion-based teachers. We introduce an Attention-based Sparse-to-Dense (AS2D) module at the front layer of the student model to enhance its ability to extract global features from sparse depth. To provide self-supervised information, we also employ multi-view depth consistency and multi-scale minimum reprojection. These techniques utilize existing structural constraints to yield supervised signals for student model training, without requiring costly ground truth depth information. Our extensive experimental evaluation demonstrates that our proposed method significantly improves the accuracy of the baseline monitored distillation method.

cs.CV↗
arXiv2022

The rational cuspidal subgroup of $J_0(p^2M)$ with $M$ squarefree

For a positive integer $N$, let $\mathscr{C}_N(\mathbb{Q})$ be the rational cuspidal subgroup of $J_0(N)$ and $\mathscr{C}(N)$ be the rational cuspidal divisor class group of $X_0(N)$, which are both subgroups of the rational torsion subgroup of $J_0(N)$. We prove that two groups $\mathscr{C}_N(\mathbb{Q})$ and $\mathscr{C}(N)$ are equal when $N=p^2M$ for any prime $p$ and any squarefree integer $M$. To achieve this we show that all modular units on $X_0(N)$ can be written as products of certain functions $F_{m, h}$, which are constructed from generalized Dedekind eta functions. Also, we determine the necessary and sufficient conditions for such products to be modular units on $X_0(N)$ under a mild assumption.

math.NT↗
arXiv2022

A superconducting nanowire photon number resolving four-quadrant detector-based Gigabit deep-space laser communication receiver prototype

Deep space explorations require transferring huge amounts of data quickly from very distant targets. Laser communication is a promising technology that can offer a data rate of magnitude faster than conventional microwave communication due to the fundamentally narrow divergence of light. This study demonstrated a photon-sensitive receiver prototype with over Gigabit data rate, immunity to strong background photon noise, and simultaneous tracking ability. The advantages are inherited from a joint-optimized superconducting nanowire single-photon detector (SNSPD) array, designed into a four-quadrant structure with each quadrant capable of resolving six photons. Installed in a free-space coupled and low-vibration cryostat, the system detection efficiency reached 72.7%, the detector efficiency was 97.5%, and the total photon counting rate was 1.6 Gcps. Additionally, communication performance was tested for pulse position modulation (PPM) format. A series of signal processing methods were introduced to maximize the performance of the forward error correction (FEC) code. Consequently, the receiver exhibits a faster data rate and better sensitivity by about twofold (1.76 photons/bit at 800 Mbps and 3.40 photons/bit at 1.2 Gbps) compared to previously reported results (3.18 photon/bit at 622 Mbps for the Lunar Laser Communication Demonstration). Furthermore, communications in strong background noise and with simultaneous tracking ability were demonstrated aimed at the challenges of daylight operation and accurate tracking of dim beacon light in deep space scenarios.

physics.ins-det↗
arXiv2021

Metrics with positive constant curvature and modular differential equations

In this paper, we consider the problem when a differential equation y"(z)=Q(z)y(z) is Fuchsian on H* and apparent on H, where Q(z) is a meromorphic modular form of weight 4 on SL(2,Z) and H denotes the complex upper half-plane. Such a problem is closely related to the problem of the existence of a conformal metric with curvature 1/2 on H.

math.CA↗
arXiv2021

Improve photon number discrimination for a superconducting series nanowire detector by applying a digital matched filter

Photon number resolving (PNR) is an important capacity for detectors working in quantum and classical applications. Although a conventional superconducting nanowire single-photon detector (SNSPD) is not a PNR detector, by arranging nanowires in a series array and multiplexing photons over space, such series PNR-SNSPD can gain quasi-PNR capacity. However, the accuracy and maximum resolved photon number are both limited by the signal-to-noise (SNR) ratio of the output pulses. Here, we introduce a matched filter, which is an optimal filter in terms of SNR for SNSPD pulses. Experimentally, compared to conventional readout using a room-temperature amplifier, the normalized spacing between pulse amplitudes from adjacent photon number detections increased by a maximum factor of 2.1 after the matched filter. Combining with a cryogenic amplifier to increase SNR further, such spacing increased by a maximum factor of 5.3. In contrast to a low pass filter, the matched filter gave better SNRs while maintaining good timing jitters. Minimum timing jitter of 55 ps was obtained experimentally. Our results suggest that the matched filter is a useful tool for improving the performance of the series PNR-SNSPD and the maximum resolved photon number can be expected to reach 65 or even large.

quant-ph↗
arXiv2021

An optics-free computational spectrometer using a broadband and tunable dynamic detector

Optical spectrometers are the central instruments for exploring the interaction between light and matter. The current pursuit of the field is to design a spectrometer without the need for wavelength multiplexing optics to effectively reduce the complexity and physical size of the hardware. Based on computational spectroscopic results and combining a broadband-responsive dynamic detector, we successfully demonstrate an optics-free single-detector spectrometer that maps the tunable quantum efficiency of a superconducting nanowire into an ill-conditioned matrix to build a solvable inverse mathematical equation. Such a spectrometer can realize a broadband spectral responsivity ranging from 660 to 1900 nm. The spectral resolution at the telecom is 6 nm, exceeding the energy resolving capacity of existing infrared single-photon detectors. Meanwhile, benefiting from the optics-free setup, precise time-of-flight measurements can be simultaneously achieved. We have demonstrated a spectral LiDAR with 8 spectral channels. This work provides a concise method for building multifunctional spectrometers and paves the way for applying superconducting nanowire detectors in spectroscopy.

physics.optics↗
arXiv2021

On class number relations, intersections, and GL(2)-tale over the function field side

The aim of this paper is to study class number relations over function fields and the intersections of Hirzebruch-Zagier type divisors on the Drinfeld-Stuhler modular surfaces. The main bridge is a particular "harmonic" theta series with nebentypus. Using the strong approximation theorem, the Fourier coefficients of this series are expressed in two ways; one comes from modified Hurwitz class numbers and another gives the intersection numbers in question. An elaboration of this approach enables us to interpret these class numbers as a "mass sum" over the CM points on the Drinfeld-Stuhler modular curves, and even realize the generating function as a metaplectic automorphic form.

math.NT↗
arXiv2020

Class numbers of CM algebraic tori, CM abelian varieties and components of unitary Shimura varieties

We give a formula for the class number of an arbitrary CM algebraic torus over $\mathbb{Q}$. This is proved based on results of Ono and Shyr. As applications, we give formulas for numbers of polarized CM abelian varieties, of connected components of unitary Shimura varieties and of certain polarized abelian varieties over finite fields. We also give a second proof of our main result.

math.NT↗
arXiv2015

Equations of hyperelliptic Shimura curves

By constructing suitable Borcherds forms on Shimura curves and using Schofer's formula for norms of values of Borcherds forms at CM-points, we determine all the equations of hyperelliptic Shimura curves $X_0^D(N)$. As a byproduct, we also address the problem of whether a modular form on Shimura curves $X_0^D(N)/W_{D,N}$ with a divisor supported on CM-divisors can be realized as a Borcherds form, where $X_0^D(N)/W_{D,N}$ denotes the quotient of $X_0^D(N)$ by all the Atkin-Lehner involutions. The construction of Borcherds forms is done by solving certain integer programming problems.

math.NT↗