The Spectrum of Multiplicative Functions
Copyright policy )The Spectrum of Multiplicative Functions
Let S be a subset of the unit disk, and let F(s) denote the class of completely multiplicative functions f such that f(p) is in S for all primes p. The authors' main concern is which numbers arise as mean-values of functions in F(s). More precisely, let Gamma_N(S) = {1/N sum_{n <= N} f(n): f in F(S)} and Gamma(S) = lim_{N -> infinity} Gamma_N(s). The authors call Gamma(S) the spectrum of the set S, and study its properties.
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- University of Georgia Press United States
- Institute for Advanced Study United States
integral equations, Mathematics - Number Theory, \(m\)th power residues, Power residues, reciprocity, FOS: Mathematics, Asymptotic results on arithmetic functions, Number Theory (math.NT), Estimates on character sums, Euler product
integral equations, Mathematics - Number Theory, \(m\)th power residues, Power residues, reciprocity, FOS: Mathematics, Asymptotic results on arithmetic functions, Number Theory (math.NT), Estimates on character sums, Euler product
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