Asymptotic growth of Hermite series and an application to the theory of the Riemann zeta function
type: Item
instance of: scholarly article
title: Asymptotic growth of Hermite series and an application to the theory of the Riemann zeta function
zbMATH Open document ID: 0871.11053
DOI: 10.1007/BF03322153
author: Markus Grawe
published in: Results in Mathematics
publication date: 1997-10-01T00:00:00Z
review text: It is shown that the Riemann hypothesis is a consequence of a growth condition for a sequence of numbers associated with Hermite functions \(h_n\), which are solutions of the second-order differential equation \[ y''(x)+(2n+1-x^2)y(x)=0. \]
reviewed by: Tom M. Apostol
Mathematics Subject Classification ID: 11M26
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 41A60
Mathematics Subject Classification ID: 42C10
zbMATH DE Number: 1003990
zbMATH Keywords: Riemann hypothesis
zbMATH Keywords: growth condition
zbMATH Keywords: Hermite functions
MaRDI profile type: Publication
cites work: Mean Convergence of Expansions in Laguerre and Hermite Series
cites work: Classical Fourier transforms
cites work: Asymptotic Solutions of Differential Equations with Transition Points or Singularities
cites work: Q5824493
cites work: Q3232759
cites work: Norm estimates for \((C,\delta)\) means of Hermite expansions and bounds for \(\delta_{eff}\)
cites work: Q4039835
cites work: Q5803461
description: scientific article; zbMATH DE number 1003990