An arithmetical approach to the convergence problem of series of dilated functions and its connection with the Riemann zeta function

DOI10.1016/j.jnt.2015.10.002zbMath1381.40004arXiv1407.2722OpenAlexW2962777992MaRDI QIDQ907480

Michel J. G. Weber

Publication date: 25 January 2016

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.2722

zbMATH Keywords

GCDRiemann zeta functionseriesarithmetical functionsalmost everywhere convergencemean convergenceDirichlet convolution\(\Omega\)-theoremdecomposition of squared sumsFC setssystems of dilated functions

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Convergence and divergence of series and sequences of functions (40A30)

Related Items (7)

Study of almost everywhere convergence of series by mean of martingale methods ⋮ On the equation \(n_1n_2 = n_3n_4\) restricted to factor closed sets ⋮ Refinements of Gál's theorem and applications ⋮ Pointwise convergence of almost periodic Fourier series and associated series of dilates ⋮ MORE ON A CERTAIN ARITHMETICAL DETERMINANT ⋮ On a certain arithmetical determinant ⋮ AN EXTENSION OF A RESULT OF ERDŐS AND ZAREMBA

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On series \(\sum c_k f(kx)\) and Khinchin's conjecture
• GCD sums from Poisson integrals and systems of dilated functions
• On systems of dilated functions
• The determinants of GCD matrices
• Dynamical systems and processes
• Sur la concentration moyenne des diviseurs. (On the mean concentration of divisors)
• Introduction to arithmetical functions
• On Smith's determinant
• Notes on the Riemann \(\zeta\)-function. IV
• Minimal Gerschgorin sets
• ON SERIES OF DILATED FUNCTIONS
• DAVENPORT SERIES AND ALMOST-SURE CONVERGENCE
• Handbook of Number Theory I
• On the convergence of ∑𝑐_{𝑘}𝑓(𝑛_{𝑘}𝑥)
• An arithmetical mapping and applications to Ω-results for the Riemann zeta function
• Matrix Analysis
• Note on some greatest common divisor matrices
• ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF GREATEST COMMON DIVISOR MATRICES
• GCD sums and complete sets of square-free numbers
• Convergence of series of dilated functions and spectral norms of GCD matrices
• Diophantine Approximations and Hilbert's Space

This page was built for publication: An arithmetical approach to the convergence problem of series of dilated functions and its connection with the Riemann zeta function