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Commentarii Mathematici Helvetici

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Volume 94, Issue 3, 2019, pp. 533–568
DOI: 10.4171/CMH/467

Published online: 2019-09-25

Fourier optimization and prime gaps

Emanuel Carneiro[1], Micah B. Milinovich[2] and Kannan Soundararajan[3]

(1) The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy and IMPA, Rio de Janeiro, Brazil
(2) University of Mississippi, University, USA
(3) Stanford University, USA

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.

Keywords: Bandlimited functions, Fourier uncertainty, prime gaps, Riemann hypothesis

Carneiro Emanuel, Milinovich Micah, Soundararajan Kannan: Fourier optimization and prime gaps. Comment. Math. Helv. 94 (2019), 533-568. doi: 10.4171/CMH/467