Fourier optimization and prime gaps

2017/08/31 by Emanuel Carneiro, Micah B. Milinovich, K. Soundararajan +1
Mathematics · #Algebraic Geometry and Number Theory #Algebraic and Geometric Analysis #Analytic Number Theory Research #Combinatorics #Connection (principal bundle) #Current (fluid) #Discrete mathematics #Fourier analysis #Fourier transform #Geometry #Mathematical analysis #Mathematics #Physics #Prime (order theory) #Pure mathematics #Riemann hypothesis #math.CA #math.NT #msc:11M06 #msc:11M26 #msc:11N05 #msc:41A30

paper · pdf · doi:10.4171/cmh/467

published as Comment. Math. Helv. 94 (2019), no. 3, 533--568 · Minor revisions in version 2; to appear in Comment. Math. Helv.; 30 pages

arxiv created 2018/09/14 · openalex publication_date 2019/09/25 · arxiv updated 2021/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

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