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Estimates for Fourier Coefficients of Cusp Forms in Weight Aspect

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Chinese Annals of Mathematics,Series B 2016年第5期37卷 793-802页

作者： hengcai tang Department of Mathematics Henan University

Let f be a holomorphic Hecke eigenform of weight k for the modular groupΓ = SL2(Z) and let λf(n) be the n-th normalized Fourier coefficient. In this paper, by a new estimate of the second integral moment of the symmetric square L-function related to f, the estimate 1λf(n21) x2 k2(log(x + k))6n≤x is established, which improves the previous result.

关键词： Forms normalized symmetric modular absolute instead Mellin inequality sufficiently approximate

The Generalized Prime Number Theorem for Automorphic L-Functions

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Chinese Annals of Mathematics,Series B 2009年第3期30卷 251-260页

作者： hengcai tang School of Mathematics Shandong University Jinan 250100 China

Let π and π' be automorphic irreducible cuspidal representations of GLm(QA) and GLm'(QA),respectively,and L(s,π×■) be the Rankin-Selberg L-function attached to π and π'.Without assuming the Generalized Ramanujan Conjecture(GRC),the author gives the generalized prime number theorem for L(s,π×■) when π≌π'.The result generalizes the corresponding result of Liu and Ye in 2007.

关键词： Perron's formula Prime number theorem Rankin-Selberg L-functions

Waring-Goldbach problem for fourth powers in short intervals

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Frontiers of Mathematics in China 2013年第6期8卷 1407-1423页

作者： hengcai tang Feng ZHAO School of Mathematics Henan University Kaifeng 475004 China College of Mathematics and Information Science North China University of Water Resources and Electric Power Zhengzhou 450011 China

We prove that almost all integers N satisfying some necessary congruence conditions are the sum of almost equal fourth prime powers.

关键词： Circle method exponential sum short interval

On the first negative Hecke eigenvalue of an automorphic representation of GL_(2)(A_(Q))

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Science China Mathematics 2021年第11期64卷 2381-2394页

作者： Yuk-Kam Lau Ming Ho Ng hengcai tang Yingnan Wang Department of Mathematics The University of Hong KongHong KongChina Department of Mathematics The Chinese University of Hong KongHong KongChina Institute of Modern Mathematics School of Mathematics and StatisticsHenan UniversityKaifeng 475004China Shenzhen Key Laboratory of Advanced Machine Learning and Applications College of Mathematics and StatisticsShenzhen UniversityShenzhen 518060China

Letπbe a self-dual irreducible cuspidal automorphic representation of GL_(2)(A_(Q))with trivial central *** Hecke eigenvalue λπ(n)is a real multiplicative function in *** show that λπ(n)<0 for some n< 详细信息

关键词： automorphic representation Hecke eigenvalue Maass cusp form sign change

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一类特殊Beatty序列中的素因子问题

数学年刊（A辑） 2010年第4期31卷 403-410页

作者：唐恒才河南大学数学与信息科学学院河南开封475004

研究了数论函数Ω和ω取值于一类特殊的非齐次Beatty序列[αn+β](n=1,2,…)的问题.特别地,证明了渐近公式■ω([αn+β)=N log log N+O(N(log log N)^(3/4))以及■(-1)^(Ω([αn+β]))=O(N/((log N)^(1/2))),其中α,β∈R,n∈Z^+,α>0... 详细信息

关键词： Beatty序列素因子数论函数

Mental Health Impacts of the COVID-19 Pandemic: Reflecting on Lockdowns and Social Isolations

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Advances in Infectious Diseases 2022年第2期12卷 193-202页

作者： Ali Cheshmehzangi Zhaohui Su Tong Zou hengcai Chen Tian tang Ayotunde Dawodu Network for Education and Research on Peace and Sustainability (NERPS) Hiroshima University Hiroshima Japan Department of Architecture and Built Environment University of Nottingham Ningbo China Ningbo China Center on Smart and Connected Health Technologies Mays Cancer Center School of Nursing UT Health San Antonio San Antonio USA Department of Science and Technology AVA Engineering Consultants Ltd. Chongqing China

This brief study explores the diverse and long-term mental impacts of the COVID-19 pandemic on societies worldwide. Based on the recent existing literature, six primary categories of mental effects are identified to verify how people are affected by reoccurring lockdowns and social isolations. The study urges holistic research in this field, suggesting that researchers must not neglect the diversity of mental health impacts and context-specific factors. While long-term mental and psychological impacts are mostly hidden for now, we anticipate them to fuel other health issues already experienced by the vulnerable groups, healthcare units, and those fighting the pandemic at the front line. The paper aims to highlight primary mental health impacts of the COVID-19 pandemic due to reoccurring lockdowns and social isolations. This is an opinion paper reflecting on ongoing research related to mental health issues of the ongoing pandemic, some of that could be looked at through case study research or extended research and comparative studies. This brief study suggests further case study-based analysis to evaluate the impacts of lockdowns and social isolations on societal wellbeing and mental health. Globally, the ongoing pandemic has made public health unstable and is expected to continue with its long-term consequences on societies. Research studies should help make governments and policymakers more aware of such long-term consequences to ensure they can respond more effectively to foreseeing public health issues.

关键词： COVID-19 Mental Health Lockdown Response Public Health Social Isolation