• Corpus ID: 240354119

The variance of integers without small prime factors in short intervals

  title={The variance of integers without small prime factors in short intervals},
  author={Ofir Gorodetsky},
Abstract The variance of primes in short intervals relates to the Riemann Hypothesis, Montgomery’s Pair Correlation Conjecture and the Hardy-Littlewood Conjecture. In regards to its asymptotics, very little is known unconditionally. We study the variance of integers without prime factors below y, in short intervals. We use sieve theory to prove an unconditional asymptotic result in a range for which we give evidence is qualitatively best possible. We find that this variance connects with… 


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