The exponential-type generating function of the Riemann zeta-function revisited
The exponential-type generating function of the Riemann zeta-function revisited
复制标题
黎曼 zeta 函数的指数型生成函数重温
DOI：
10.1007/s11139-022-00644-7
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发表时间：
2023
期刊：
影响因子：
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通讯作者：
Takumi Noda
中科院分区：
文献类型：
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作者：
Hanaki Akihide;Hirai Takuto;Ponomarenko Ilia;花木章秀;Takumi Noda
介绍了狄利克雷级数与庞卡罗级数的关系。给出了黎曼ζ函数的指数型生成函数Voronoï-type的积分表示和变换公式。作为应用，给出了全纯庞卡罗级数的傅里叶级数展开式的一个新的证明。
Dirichlet series associated with the Poincaré series attached toare introduced. Integral representations and transformation formulas are given, which describe the Voronoï-type summation formula for the exponential-type generating function of the Riemann zeta-function. As an application, a new proof of the Fourier series expansion of holomorphic Poincaré series is given.