数论团队成员—王丹

发布者:数学与统计学院发布时间:2023-12-29浏览次数:640


王丹,讲师。于2020年获山东大学基础数学博士学位,现为齐鲁工业大学(山东省科学院)数学与人工智能学部教师。近几年主要从事解析数论、计算数论等方面的研究工作,主持国家自然科学基金青年基金1项,山东省自然科学基金青年基金1项、面上项目1项,校级培新项目1项,发表论文10余篇。

 

研究方向:自守函数傅里叶系数的均值估计、经典解析数论中的算术函数均值估计问题等

 

承担科研项目情况

1.国家自然科学基金青年项目,12401008, 高阶群上自守形式傅里叶系数的移位卷积和及扭乘和估计,2025.1.1-2027.12.31,30万,主持

2.山东省自然科学基金面上项目,ZR2024MA044,高阶群上自守形式和自守L-函数解析理论研究,2025.01.01-2027.12.31,10万,主持

3. 山东省自然科学基金青年基金项目,ZR2021QA060,有关算术函数均值估计的若干问题,2022.01.01-2024.12.3115万元, 主持。

2. 齐鲁工业大学(山东省科学院)科教产试点工程基础研究类项目(培新项目),2023PX080,自守形式傅里叶系数的均值估计及应用,2023.01.01-2024.12.3110万,主持。

 

部分代表性论文

[1] Dan Wang, On general divisor problems involving Hecke eigenvaluesActa Math Hungar. 153(2017), 2,509-523.

[2] Guangshi Lv and Dan Wang(通讯作者), Averages of shifted convolutions of general divisor sums involving Hecke eigenvalues, Journal of Number Theory 199(2019),342-351.

[3] Guangshi Lv and Dan Wang(通讯作者), Shifted convolution sums of Fourier coefficients with squarefull kernel functions, Lithuanian Mathematical Journal.60(2020),51-63. 4322-4335.

[4] Dan Wang, The Selberg-Delange method in short intervals about Dedekind zeta function, Acta Arithmetica. 192.3(2020),301-311.

[5] Huixue Lao, Zhenxing Xie, Dan Wang, On the number of representations of integers by quaternary quadratic forms, Indian Journal of Pure and Applied Mathematics,2021.

[6] Dan Wang, On the sum of two squares and at most k powers, Integer. 2021.

[7] Dan Wang, An improvement on the perfect order subsets of finite groups, Indian Journal of Pure and Applied Mathematics, 2021.

[8] Dan Wang, On the distribution of squarefull integers, Indian Journal of Pure and Applied Mathematics, 2021.

[9] Dan Wang, Averages of shifted convolutions of general divisor sums involving Hecke eigenvalues,Indian Journal of Pure and Applied Mathematics, 2021.

[10] Dan Wang, Sums of Fourier coefficients of holomorphic cusp forms over integers without large prime factors,Indian Journal of Pure and Applied Mathematics, 2022.

[11] Dan Wang, Weighted Erdös-Kac type theorems in short intervals, Acta Arithmetica, 2023.