On instances of Fox’s integral equation connection to the Riemann zeta function

Alexander E. Patkowski

Displaying similar documents to “On instances of Fox’s integral equation connection to the Riemann zeta function”

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Aleksandar Ivić (1989)

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Habiba Kadiri (2013)

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We prove an explicit bound for N(σ,T), the number of zeros of the Riemann zeta function satisfying ℜ𝔢 s ≥ σ and 0 ≤ ℑ𝔪 s ≤ T. This result provides a significant improvement to Rosser's bound for N(T) when used for estimating prime counting functions.

Note on a paper by H. L. Montgomery (Omega theorems for the Riemann zeta- function).

Ramachandra, K., Sankaranarayanan, A. (1991)

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Norman Levinson (1972)

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A. Laurinčikas (1990)

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Almkvist, Gert, Granville, Andrew (1999)

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Masatoshi Suzuki (2013)

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We introduce a family of deformations of the Riemann xi-function endowed with two continuous parameters. We show that it has rich analytic structure and that its conjectural (mild) zero-free region for some fixed parameter is a sufficient condition for the Riemann hypothesis to hold for the Riemann zeta function.

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Daniel Bump, Eugene K.-S. Ng (1986)

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Mean values of the Riemann zeta-function and its derivatives.

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Correction to: "On a positivity property of the Riemann ξ-function" (Acta Arith. 89 (1999), 217-234)

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