Fourier optimization and prime gaps

Emanuel Carneiro; Micah B. Milinovich; Kannan Soundararajan

doi:10.4171/cmh/467

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
- MathSciNet
- zbMATH Open
Micah B. Milinovich
University of Mississippi, University, USA
- MathSciNet
- zbMATH Open
Kannan Soundararajan
Stanford University, USA
- MathSciNet
- zbMATH Open

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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