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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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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)-...
Alessandro Languasco's user avatar

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