After studying Cesaro and Borel summation i think that(adsbygoogle = window.adsbygoogle || []).push({});

sum [tex] \sum_{p} p^{k} [/tex] extended over all primes is summable Cesaro [tex] C(n,k+1+\epsilon) [/tex]

and the series [tex] \sum_{n=0}^{\infty} M(n) [/tex] and [tex] \sum_{n=0}^{\infty} \Psi (n)-n [/tex]

are Cesaro-summable [tex] C(n,3/2+\epsilon) [/tex] for any positive epsilon

hence the fact that M(0)+M(1)+M(2)+............... is Cearo summable 3/2+e is a consequence of Riemann Hypothesis.

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# A conjecture on Cesaro summation and primes.

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