English

On a conjecture of Montgomery and Soundararajan

Number Theory 2020-09-15 v1

Abstract

We establish lower bounds for all weighted even moments of primes up to XX in intervals which are in agreement with a conjecture of Montgomery and Soundararajan. Our bounds hold unconditionally for an unbounded set of values of XX, and hold for all XX under the Riemann Hypothesis. We also deduce new unconditional Ω\Omega-results for the classical prime counting function.

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Cite

@article{arxiv.2009.05760,
  title  = {On a conjecture of Montgomery and Soundararajan},
  author = {Régis de la Bretèche and Daniel Fiorilli},
  journal= {arXiv preprint arXiv:2009.05760},
  year   = {2020}
}

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15 pages