Prime gaps and gaps between successive critical zeros of zeta

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Assuming RH, the sequence of critical zeros of the Riemann zeta function can be viewed as the Fourier transform of the sequence of primes. From a physicist point of view, the average gap between the elements of a sequence of points on a straight line is the reciprocal of the average gap of the sequence obtained through the application of the Fourier transform, up to a normalisation factor of $ 2pi $.
Is there thus a heuristics suggesting that the proportion of integers n below x such that $aleqdfracp_n+1-p_nlog p_n leq b$ is equal to the proportion of critical Riemann zeros $ 1/2+igamma_n $ of imaginary part less than T such that $dfrac2pibleq (gamma_n+1-gamma_n)loggamma_nleqdfrac2pia $ with $ 0lt alt bltinfty $?




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    Assuming RH, the sequence of critical zeros of the Riemann zeta function can be viewed as the Fourier transform of the sequence of primes. From a physicist point of view, the average gap between the elements of a sequence of points on a straight line is the reciprocal of the average gap of the sequence obtained through the application of the Fourier transform, up to a normalisation factor of $ 2pi $.
    Is there thus a heuristics suggesting that the proportion of integers n below x such that $aleqdfracp_n+1-p_nlog p_n leq b$ is equal to the proportion of critical Riemann zeros $ 1/2+igamma_n $ of imaginary part less than T such that $dfrac2pibleq (gamma_n+1-gamma_n)loggamma_nleqdfrac2pia $ with $ 0lt alt bltinfty $?




    number-theory fourier-transform riemann-zeta prime-gaps




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      Assuming RH, the sequence of critical zeros of the Riemann zeta function can be viewed as the Fourier transform of the sequence of primes. From a physicist point of view, the average gap between the elements of a sequence of points on a straight line is the reciprocal of the average gap of the sequence obtained through the application of the Fourier transform, up to a normalisation factor of $ 2pi $.
      Is there thus a heuristics suggesting that the proportion of integers n below x such that $aleqdfracp_n+1-p_nlog p_n leq b$ is equal to the proportion of critical Riemann zeros $ 1/2+igamma_n $ of imaginary part less than T such that $dfrac2pibleq (gamma_n+1-gamma_n)loggamma_nleqdfrac2pia $ with $ 0lt alt bltinfty $?




      number-theory fourier-transform riemann-zeta prime-gaps




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      Assuming RH, the sequence of critical zeros of the Riemann zeta function can be viewed as the Fourier transform of the sequence of primes. From a physicist point of view, the average gap between the elements of a sequence of points on a straight line is the reciprocal of the average gap of the sequence obtained through the application of the Fourier transform, up to a normalisation factor of $ 2pi $.
      Is there thus a heuristics suggesting that the proportion of integers n below x such that $aleqdfracp_n+1-p_nlog p_n leq b$ is equal to the proportion of critical Riemann zeros $ 1/2+igamma_n $ of imaginary part less than T such that $dfrac2pibleq (gamma_n+1-gamma_n)loggamma_nleqdfrac2pia $ with $ 0lt alt bltinfty $?





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      Sylvain Julien

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