数学季刊

高阶除数函数在混合幂次上的值

都晨豪, 孙庆峰

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 ……

有限整数和集问题研究综述

汤敏

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.

Dirichlet L-函数的均值

黄炳荣, 黄俊皓

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.

涉及二项式系数的新级数 (III)

孙智伟

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……

华林问题及其部分相关问题的综述

赵立璐

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.

Hecke-Maass新形式的Hecke特征值的第一个变号问题

唐恒才, 王英男

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.

双曲超曲面与费马型函数方程

陶思俊, 谢利兵, 陈裕先

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 CP³ and CP⁴, and discusses the existence of solutions for a class of Fermat type functional equations.

一类高阶基尔霍夫方程的适定性和渐近性质

张辽, 李锋杰

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.

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