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• W2955372169 abstract "This paper outlines further properties concerning the fractional derivative of the Riemann ζ function. The functional equation, computed by the introduction of the Grünwald–Letnikov fractional derivative, is rewritten in a simplified form that reduces the computational cost. Additionally, a quasisymmetric form of the aforementioned functional equation is derived (symmetric up to one complex multiplicative constant). The second part of the paper examines the link with the distribution of prime numbers. The Dirichlet η function suggests the introduction of a complex strip as a fractional counterpart of the critical strip. Analytic properties are shown, particularly that a Dirichlet series can be linked with this strip and expressed as a sum of the fractional derivatives of ζ. Finally, Theorem 4.3 links the fractional derivative of ζ with the distribution of prime numbers in the left half-plane." @default.
• W2955372169 created "2019-07-12" @default.
• W2955372169 creator A5005852879 @default.
• W2955372169 date "2019-07-02" @default.
• W2955372169 modified "2023-10-14" @default.
• W2955372169 title "Riemann zeta fractional derivative—functional equation and link with primes" @default.
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• W2955372169 doi "https://doi.org/10.1186/s13662-019-2202-5" @default.
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