Produção Nacional
Revisado por pares
Bandlimited approximations and estimates for the Riemann zeta-function
2019; Autonomous University of Barcelona; Volume: 63; Linguagem: Inglês
10.5565/publmat6321906
ISSN2014-4350
AutoresEmanuel Carneiro, Andrés Chirre, Micah B. Milinovich,
Tópico(s)Mathematical functions and polynomials
ResumoIn this paper, we provide explicit upper and lower bounds for the argument of the Riemann zeta-function and its antiderivatives in the critical strip under the assumption of the Riemann hypothesis. This extends the previously known bounds for these quantities on the critical line (and sharpens the error terms in such estimates). Our tools come not only from number theory, but also from Fourier analysis and approximation theory. An important element in our strategy is the ability to solve a Fourier optimization problem with constraints, namely, the problem of majorizing certain real-valued even functions by bandlimited functions, optimizing the $L^1(\mathbb{R})-$error. Deriving explicit formulae for the Fourier transforms of such optimal approximations plays a crucial role in our approach.
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