Chinese Quarterly Journal of Mathematics

Current Issue

30 December 2025, Volume 40 Issue 4

Previous Issue

Higher Order Divisor Functions over Values of Mixed Powers#br#

DU Chen-hao, SUN Qing-feng

2025, 40(4): 331-351.

doi:10.13371/j.cnki.chin.q.j.m.2025.04.001

Asbtract ( 21 )

PDF (451KB) ( 10 )

Related Articles | Metrics

Let τ_k(n) be the k-th divisor function. In this paper, we derive an asymptotic formula for the sum ……

A Survey on Sumset Problems of Finite Integer Sets

TANG Min

2025, 40(4): 352-359.

doi:10.13371/j.cnki.chin.q.j.m.2025.04.002

Asbtract ( 27 )

PDF (309KB) ( 7 )

Related Articles | Metrics

Let A be a finite set of integers. For any integer h≥2, let hA and h ^∧A be the sets of all sums of h elements of A and all sums of h distinct elements of A, respectively. In this paper, we survey some significant advances in additive combinatorics concerning the size and structure of sumsets of finite integer sets.

Moments of Dirichlet L-Functions

HUANG Bing-rong, HUANG Jun-hao

2025, 40(4): 360-371.

doi:10.13371/j.cnki.chin.q.j.m.2025.04.003

Asbtract ( 54 )

PDF (346KB) ( 30 )

Related Articles | Metrics

In this paper, we establish asymptotic formulas for a cubic moment of Dirichlet L-functions restricted to a coset, as well as for a mixed moment of Dirichlet L-functions and twists of GL(2) L-functions along a coset. Our main tool is a power-saving estimate of bilinear forms of hyper-Kloosterman sums due to Kowalski–Michel–Sawin.

New Series Involving Binomial Coefficients (III)

SUN Zhi-wei

2025, 40(4): 372-392.

doi:10.13371/j.cnki.chin.q.j.m.2025.04.004

Asbtract ( 17 )

PDF (428KB) ( 3 )

Related Articles | Metrics

We evaluate some series with summands involving a single binomial coefficien……

A Survey on Waring’s Problem and Some Related Topics

ZHAO Li-lu

2025, 40(4): 393-400.

doi:10.13371/j.cnki.chin.q.j.m.2025.04.005

Asbtract ( 28 )

PDF (323KB) ( 8 )

Related Articles | Metrics

The aim of this survey is to introduce Waring’s problem and some related topics including mean value theorems and Diophantine equations in prime variables.

The First Sign Change of Hecke Eigenvalues of Hecke-Maass New Forms#br#

TANG Heng-cai, WANG Ying-nan

2025, 40(4): 401-407.

doi:10.13371/j.cnki.chin.q.j.m.2025.04.006

Asbtract ( 23 )

PDF (349KB) ( 8 )

Related Articles | Metrics

In this short note, we survey the recent development on the first sign change of Hecke eigenvalues of Hecke-Maass new forms.

Hyperbolic Hypersurfaces and Fermat Type Functional Equation#br#

TAO Si-jun, XIE Li-bing, CHEN Yu-xian

2025, 40(4): 408-416.

doi:10.13371/j.cnki.chin.q.j.m.2025.04.007

Asbtract ( 22 )

PDF (353KB) ( 8 )

Related Articles | Metrics

In this paper, we construct new examples of hyperbolic metasurfaces in CP³ and CP⁴, and discusses the existence of solutions for a class of Fermat type functional equations.

Well-Posedness and Asymptotic Behavior of a Higher-Order Kirchhoff Equation#br#

ZHANG Liao, LI Feng-jie

2025, 40(4): 417-440.

doi:10.13371/j.cnki.chin.q.j.m.2025.04.008

Asbtract ( 15 )

PDF (437KB) ( 10 )

Related Articles | Metrics

This paper focuses on the investigation of a hyperbolic Kirchhoff equation with nonlinear damping and higher-order dissipation terms. Initially, the existence and uniqueness of local weak solutions are rigorously established. Next, within the framework of potential well theory, the classification of solution behaviors, including blow-up and global existence, is systematically analyzed according to the relationships among the exponents of nonlinear source terms. Finally, explicit bounds for the blow-up time and decay estimates for global solutions are presented.