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Table of Content
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
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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
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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
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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
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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
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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
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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
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In this paper, we construct new examples of hyperbolic metasurfaces in CP
3
and CP
4
, 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
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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.
