On mean values of random multiplicative functions

DOI10.1090/S0002-9939-2012-11332-2zbMath1294.11167MaRDI QIDQ4908256

Jie Wu, Yuk-Kam Lau, Gérald Tenenbaum

Publication date: 5 March 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Möbius functionlaw of iterated logarithmRademacher functionmean values of multiplicative functionsrandom multiplicative function

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Strong limit theorems (60F15) Probabilistic theory: distribution modulo (1); metric theory of algorithms (11K99)

Related Items (21)

An almost sure upper bound for random multiplicative functions on integers with a large prime factor ⋮ Partial sums of biased random multiplicative functions ⋮ On consecutive values of random completely multiplicative functions ⋮ A model problem for multiplicative chaos in number theory ⋮ Almost sure lower bounds for a model problem for multiplicative chaos in number theory ⋮ Some open questions in analysis for Dirichlet series ⋮ Sign changes of the partial sums of a random multiplicative function ⋮ Multiplicative functions resembling the Möbius function ⋮ On the random Chowla conjecture ⋮ Zeta functions and asymptotic additive bases with some unusual sets of primes ⋮ Central limit theorems for random multiplicative functions ⋮ Extreme values of Dirichlet polynomials with multiplicative coefficients ⋮ Better than square-root cancellation for random multiplicative functions ⋮ Bounds on the suprema of Gaussian processes, and omega results for the sum of a random multiplicative function ⋮ A Note on Helson’s Conjecture on Moments of Random Multiplicative Functions ⋮ Moments of random multiplicative functions. II: High moments ⋮ MOMENTS OF RANDOM MULTIPLICATIVE FUNCTIONS, I: LOW MOMENTS, BETTER THAN SQUAREROOT CANCELLATION, AND CRITICAL MULTIPLICATIVE CHAOS ⋮ A note on multiplicative functions resembling the Möbius function ⋮ Random multiplicative functions: the Selberg-Delange class ⋮ Multiplicative functions supported on the \(k\)-free integers with small partial sums ⋮ Partial sums of random multiplicative functions and extreme values of a model for the Riemann zeta function

Cites Work

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• The distribution of values of \(L(1,\chi_d)\)
• Bounds on the suprema of Gaussian processes, and omega results for the sum of a random multiplicative function
• Note on a paper by A. Granville and K. Soundararajan
• Étude des coefficients de Fourier des fonctions de \(L^ p(G)\)
• Random factorizations and Riemann's hypothesis
• Random Multiplicative Functions in Short Intervals
• Partial sums of the Möbius function

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