The Mellin transform of powers of the zeta-function
The Mellin transform of powers of the zeta-function
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DOI：
10.4064/aa-95-4-305-342
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发表时间：
2000
期刊：
影响因子：
0.7
通讯作者：
A. Ivic;M. Jutila;Y. Motohashi
中科院分区：
文献类型：
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作者：
A. Ivic;M. Jutila;Y. Motohashi
0 f（x）xs 1dx其中s = +它表示f（x）的梅林变换。梅林变换在解析数论中起着重要的作用。通过变量的变换，它们可以被看作是傅里叶变换的特殊情况，它们的性质可以从傅里叶变换的一般理论中推导出来。对于一个广泛的帐户，我们建议读者E。C. Titchmarsh（25）. Mellin变换的一个基本性质是求逆公式12 {f（x + 0）+f（x 0）} = 12 i（）F（s）xsds = 12 i lim T！1 +iT
0 f(x)x s 1 dx with s = + it denote the Mellin transform of f(x). Mellin transforms play a fundamental role in Analytic Number Theory. They can be viewed, by a change of variable, as special cases of Fourier transforms, and their properties can be deduced from the general theory of Fourier transforms. For an extensive account, we refer the reader to E. C. Titchmarsh (25). One of the basic properties of Mellin transforms is the inversion formula 1 2 {f(x + 0) +f(x 0)} = 1 2i ( ) F (s)x s ds = 1 2i lim T!1 +iT