prime number theorem;
Tauberian theorems;
integral oper-ators;
D O I:
10.15407/mag19.01.172
中图分类号:
O29 [应用数学];
学科分类号:
070104 ;
摘要:
We establish an operator theoretic version of the Wiener-Ikehara Taub e-rian theorem and use it to obtain a short proof of the Prime number theorem that should be accessible to anyone with a basic knowledge of operator the-ory and Fourier analysis.
机构:
Chinese Acad Sci, Hua Loo Keng Ctr Math Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R ChinaChinese Acad Sci, Hua Loo Keng Ctr Math Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Wang, Biao
Wei, Zhining
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机构:
Ohio State Univ, Dept Math, Columbus, OH 43210 USAChinese Acad Sci, Hua Loo Keng Ctr Math Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Wei, Zhining
Yan, Pan
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机构:
Univ Arizona, Dept Math, Tucson, AZ 85721 USAChinese Acad Sci, Hua Loo Keng Ctr Math Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Yan, Pan
Yi, Shaoyun
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机构:
Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R ChinaChinese Acad Sci, Hua Loo Keng Ctr Math Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
机构:
Nicolaus Copernicus Univ, Fac Math & Comp Sci, Ul Chopina 12-18, PL-87100 Torun, PolandNicolaus Copernicus Univ, Fac Math & Comp Sci, Ul Chopina 12-18, PL-87100 Torun, Poland
Fraczek, Krzysztof
Kanigowski, Adam
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机构:
Univ Maryland, Dept Math, 4176 Campus Dr,William E Kirwan Hall, College Pk, MD 20742 USANicolaus Copernicus Univ, Fac Math & Comp Sci, Ul Chopina 12-18, PL-87100 Torun, Poland
Kanigowski, Adam
Lemanczyk, Mariusz
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机构:
Nicolaus Copernicus Univ, Fac Math & Comp Sci, Ul Chopina 12-18, PL-87100 Torun, PolandNicolaus Copernicus Univ, Fac Math & Comp Sci, Ul Chopina 12-18, PL-87100 Torun, Poland