RT Journal Article
T1 Distribution of primes and approximation on weighted Dirichlet spaces
A1 Gallardo Gutiérrez, Eva Antonia
A1 Seco, Daniel
AB We study zero-free regions of the Riemann zeta function ζ related to an approximation problem in the weighted Dirichlet space D−2 which is known to be equivalent to the Riemann Hypothesis since the work of B ́aez-Duarte. We prove, indeed, that analogous approximation problems for the standard weighted Dirichlet spaces Dα when α ∈ (−3, −2) give conditions so that the half-plane {s ∈ C : R(s) > − α+12} is also zero-free for ζ. Moreover, we extend such results to a large family of weighted spaces of analytic functions lp α. As a particular instance, in the limit case p = 1 and α = −2, we provide a new proof of the Prime Number Theorem.
YR 2022
FD 2022
LK https://hdl.handle.net/20.500.14352/71714
UL https://hdl.handle.net/20.500.14352/71714
LA eng
NO Ministerio de Ciencia, Innovación y Universidades (España)
NO Centro de Excelencia Severo Ochoa
NO Comunidad de Madrid / V Programa regional de Investigación y Innovación tecnológica
DS Docta Complutense
RD 10 may 2025