Möbius convolutions and the Riemann hypothesis | Zendy

Luis BáezDuarte | Zendy

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Möbius convolutions and the Riemann hypothesis

Author(s) -

Luis BáezDuarte

Publication year - 2005

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/ijmms.2005.3599

Subject(s) - mathematics , convolution (computer science) , pure mathematics , riemann hypothesis , order (exchange) , class (philosophy) , function (biology) , mathematical analysis , finance , machine learning , artificial intelligence , evolutionary biology , artificial neural network , computer science , economics , biology

The well-known necessary and sufficient criteria for the Riemannhypothesis of M. Riesz and of Hardy and Littlewood, based on the order of certainentire functions on the positive real axis, are here embedded in ageneral theorem for a class of entire functions, which in turn isseen to be a consequence of a rather transparent convolutioncriterion. Some properties of the convolutions involved sharpenwhat is hitherto known for the Riesz function

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