10
votes
Accepted
Prime differences and zero multiplicity
This problem is connected with the L^2 average of primes in short intervals, see Selberg (1942 paper entitled “on the normal density…”). In particular, results on the integral of $\psi(x+h)-\psi(x)-h$ ...
7
votes
Prime differences and zero multiplicity
It is not know that RH implies EH, or that EH implies RH. Let us denote
$$S(x):=\sum_{p_n < x} (p_n -p_{n-1})^2.$$
Assuming the Lindelöf hypothesis, Yu (1996) proved that $S(x)\ll_\varepsilon x^{1+\...
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