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Title
Japanese: 
English:Mean-periodicity and zeta functions 
Author
Japanese: Ivan Fesenko, Guillaume Ricotta, 鈴木 正俊.  
English: Ivan Fesenko, Guillaume Ricotta, Masatoshi Suzuki.  
Language English 
Journal/Book name
Japanese: 
English:Annales de L'Institut Fourier 
Volume, Number, Page vol. 62    no. 5    pp. 1819-1887
Published date 2012 
Publisher
Japanese: 
English: 
Conference name
Japanese: 
English: 
Conference site
Japanese: 
English: 
Official URL http://aif.cedram.org/aif-bin/item?id=AIF_2012__62_5_1819_0
 
DOI https://doi.org/10.5802/aif.2737
Abstract This paper establishes new bridges between zeta functions in number theory and modern harmonic analysis, namely between the class of complex functions, which contains the zeta functions of arithmetic schemes and closed with respect to product and quotient, and the class of mean-periodic functions in several spaces of functions on the real line. In particular, the meromorphic continuation and functional equation of the zeta function of an arithmetic scheme with its expected analytic shape is shown to correspond to mean-periodicity of a certain explicitly defined function associated to the zeta function. The case of elliptic curves over number fields and their regular models is treated in more details, and many other examples are included as well.

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