GCD sums from Poisson integrals and systems of dilated functions

DOI10.4171/JEMS/537zbMath1344.11053arXiv1210.0741OpenAlexW2963374055MaRDI QIDQ496455

Kristian Seip, Christoph Aistleitner, István Berkes

Publication date: 21 September 2015

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.0741

zbMATH Keywords

polydiscPoisson integralspectral normCarleson-Hunt inequalityconvergence of series of dilated functionsGCD sums and matrices

Mathematics Subject Classification ID

Convergence and absolute convergence of Fourier and trigonometric series (42A20) Irregularities of distribution, discrepancy (11K38) Matrices, determinants in number theory (11C20)

Related Items (27)

Gál-type GCD sums beyond the critical line ⋮ Lower bounds for the maximum of the Riemann zeta function along vertical lines ⋮ The Lerch zeta function. IV: Hecke operators ⋮ On the law of the iterated logarithm for trigonometric series with bounded gaps. II ⋮ ``Quasi-norm of an arithmetical convolution operator and the order of the Riemann zeta function ⋮ ADDITIVE ENERGY AND THE METRIC POISSONIAN PROPERTY ⋮ Refinements of Gál's theorem and applications ⋮ On convergence almost everywhere of series of dilated functions ⋮ Additive energy and the Hausdorff dimension of the exceptional set in metric pair correlation problems ⋮ Almost everywhere convergence questions of series of translates of non-negative functions ⋮ Extreme values of derivatives of the Riemann zeta function ⋮ On evil Kronecker sequences and lacunary trigonometric products ⋮ Some open questions in analysis for Dirichlet series ⋮ Random walks on the circle and Diophantine approximation ⋮ The distribution of values of zeta and \(L\)-functions ⋮ An arithmetical approach to the convergence problem of series of dilated functions and its connection with the Riemann zeta function ⋮ Note on the Resonance Method for the Riemann Zeta Function ⋮ On series \(\sum c_k f(kx)\) and Khinchin's conjecture ⋮ Mini-workshop: Interplay between number theory and analysis for Dirichlet series. Abstracts from the mini-workshop held October 29 -- November 4, 2017 ⋮ A pair correlation problem, and counting lattice points with the zeta function ⋮ GCD sums and complete sets of square-free numbers ⋮ METRIC RESULTS ON THE DISCREPANCY OF SEQUENCES MODULO ONE FOR INTEGER SEQUENCES OF POLYNOMIAL GROWTH ⋮ An optimization problem concerning multiplicative functions ⋮ GCD sums and sum-product estimates ⋮ Small Gál sums and applications ⋮ Convergence of series of dilated functions and spectral norms of GCD matrices ⋮ Metric results on summatory arithmetic functions on Beatty sets

Cites Work

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• On series \(\sum c_k f(kx)\) and Khinchin's conjecture
• A Hilbert space of Dirichlet series and systems of dilated functions in \(L^ 2(0,1)\)
• A uniform law of the iterated logarithm for classes of functions
• On convergence and growth of partial sums of Fourier series
• Convergence of $∑c_{k} f(k x)$ and the Lip $𝛼$ class
• ON SERIES OF DILATED FUNCTIONS
• Representing Measures and Hardy Spaces for the Infinite Polydisk Algebra
• DAVENPORT SERIES AND ALMOST-SURE CONVERGENCE
• On the convergence of ∑𝑐_{𝑘}𝑓(𝑛_{𝑘}𝑥)
• An arithmetical mapping and applications to Ω-results for the Riemann zeta function
• Sums Involving Common Divisors
• Some theorems in the metric theory of diophantine approximation
• Metric Number Theory and the Large Sieve
• On the asymptotic behaviour of ?f(nkx)
• SOME CASES OF THE DUFFIN AND SCHAEFFER CONJECTURE
• The Size of Trigonometric and Walsh Series and Uniform Distribution Mod 1
• On the convergence of ∑𝑐_{𝑛}𝑓(𝑛𝑥) and the Lip 1/2 class
• LACUNARY SERIES AND INDEPENDENT FUNCTIONS

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