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