JournalscmhVol. 94, No. 3pp. 533–568

Fourier optimization and prime gaps

  • Emanuel Carneiro

    The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy and IMPA, Rio de Janeiro, Brazil

  • Micah B. Milinovich

    University of Mississippi, University, USA

  • Kannan Soundararajan

    Stanford University, USA
Fourier optimization and prime gaps cover
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Abstract

We investigate some extremal problems in Fourier analysis and their connection to a problem in prime number theory. In particular, we improve the current bounds for the largest possible gap between consecutive primes assuming the Riemann hypothesis.

Cite this article

Emanuel Carneiro, Micah B. Milinovich, Kannan Soundararajan, Fourier optimization and prime gaps. Comment. Math. Helv. 94 (2019), no. 3, pp. 533–568

DOI 10.4171/CMH/467