@Article{Zaccagnini1998,
  Author = "A. Zaccagnini",
  Title  = "Primes in almost all short intervals",
  Journal = "Acta Arith.",
  Volume = "84.3",
  Pages = "225--244",
  Year = 1998,
  Abstract = "We prove the estimate $J(x,h)=o\left(xh^2(\log x)^{-2} \right)$ 
    for the Selberg integral 
    $$
    J(x,h)
    :=
    \int_x^{2x}
      \left| \pi(t) - \pi(t-h) - \frac h{\log t} \right| ^2 \, dt,
    $$
    when $h\ge x^{1/6-\varepsilon(x)}$, provided that $\varepsilon(x)\to0$ 
    as $x\to+\infty$. 
    The proof depends on an identity of Linnik and Heath-Brown which yields 
    a suitable Dirichlet series decomposition for the quantity that we want 
    to estimate. 
    This is in a form that can be attacked by means of mean value theorems for 
    Dirichlet series."
}