Trace formula in noncommutative Geometry and the zeros of the Riemann zeta function

Alain Connes

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Displaying similar documents to “Trace formula in noncommutative Geometry and the zeros of the Riemann zeta function”

Pair correlation of the zeros of the Riemann zeta function in longer ranges

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Large gaps between consecutive zeros of the Riemann zeta-function. II

H. M. Bui (2014)

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Assuming the Riemann Hypothesis we show that there exist infinitely many consecutive zeros of the Riemann zeta-function whose gaps are greater than 2.9 times the average spacing.

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Dinesh S. Thakur (1995)

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A zero density result for the Riemann zeta function

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.

Zeta functions for the Riemann zeros

André Voros (2003)

Annales de l’institut Fourier

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A family of Zeta functions built as Dirichlet series over the Riemann zeros are shown to have meromorphic extensions in the whole complex plane, for which numerous analytical features (the polar structures, plus countably many special values) are explicitly displayed.