Fourier optimization and prime gaps

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.

Minor revisions in version 2; to appear in Comment. Math. Helv.; 30 pages

References in corpus (8)

• New upper bounds on sphere packings I
• The sphere packing problem in dimension 24
• The sphere packing problem in dimension 8
• Gaussian Subordination for the Beurling-Selberg Extremal Problem
• Hilbert spaces and the pair correlation of zeros of the Riemann zeta-function
• Extremal functions in de Branges and Euclidean spaces
• Bounding $S_n(t)$ on the Riemann hypothesis
• Primes in explicit short intervals on RH

Cited by in corpus (13)

• Primes between consecutive powers
• Explicit Interval Estimates for Prime Numbers
• Estimates of the asymptotic Nikolskii constants for spherical polynomials
• Point evaluation in Paley--Wiener spaces
• Variants on Andrica's conjecture with and without the Riemann hypothesis
• The sequence of prime gaps is graphic
• New Sign Uncertainty Principles
• Cyclotomic polynomials with prescribed height and prime number theory
• Mills' constant is irrational
• The Hörmander--Bernhardsson extremal function: A preliminary study
• Topological properties and algebraic independence of sets of prime-representing constants
• Pair correlation for Dedekind zeta functions of abelian extensions
• Elliptic curves over Hasse pairs