Decay of Mean Values of Multiplicative Functions

DOI10.4153/CJM-2003-047-0zbMath1047.11093arXivmath/9911246MaRDI QIDQ4454046

Andrew Granville, Kannan Soundararajan

Publication date: 7 March 2004

Published in: Canadian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9911246

zbMATH Keywords

integral equationsexplicit upper boundsmean value of multiplicative functions

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Distribution functions associated with additive and positive multiplicative functions (11N60) Rate of growth of arithmetic functions (11N56)

Related Items (24)

A footnote to a theorem of Halász ⋮ Multiplicative functions in short intervals ⋮ A more intuitive proof of a sharp version of Halász’s theorem ⋮ ON BINARY CORRELATIONS OF MULTIPLICATIVE FUNCTIONS ⋮ On multiplicative functions which are small on average ⋮ On consecutive values of random completely multiplicative functions ⋮ Divisor-bounded multiplicative functions in short intervals ⋮ Multiplicative functions in short arithmetic progressions ⋮ Three conjectures about character sums ⋮ A refinement of the Burgess bound for character sums ⋮ Effective means for complex multiplicative functions ⋮ Large sums of high‐order characters ⋮ Mean values of multiplicative functions over function fields ⋮ A note on Halász's theorem in \(\mathbb{F}_q[t\)] ⋮ THE LOGARITHMICALLY AVERAGED CHOWLA AND ELLIOTT CONJECTURES FOR TWO-POINT CORRELATIONS ⋮ Large character sums: Burgess's theorem and zeros of \(L\)-functions ⋮ Generalized Fourier coefficients of multiplicative functions ⋮ Asymptotics for multilinear averages of multiplicative functions ⋮ Completely multiplicative functions taking values in ${-1,1}$ ⋮ Multiplicative functions in arithmetic progressions ⋮ A new proof of Halász’s theorem, and its consequences ⋮ Pretentious multiplicative functions and the prime number theorem for arithmetic progressions ⋮ Pretentiously detecting power cancellation ⋮ Additive functions in short intervals, gaps and a conjecture of Erdős

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