On the symmetry of primes

Details On the symmetry of primes On the symmetry of primes

2010-09-29

arxiv.org/abs/1009.6121v9

Mathematics

Number Theory

The paper has been withdrawn by the Author see 1103.4451v2 comments

Scientific paper

We prove a kind of "almost all symmetry" result for the primes, i.e. we give non-trivial bounds for the "symmetry integral", say $I_{\Lambda}(N,h)$, of the von Mangoldt function $\Lambda(n)$ ($:= \log p$ for prime-powers $n=p^r$, 0 otherwise). We get $I_{\Lambda}(N,h)\ll NhL^5+Nh^{21/20}L^2$, with $L:=\log N$; as a Corollary, we bound non-trivially the Selberg integral of the primes, i.e. the mean-square of $\sum_{x

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