The Spectrum of Multiplicative Functions
نویسندگان
چکیده
Dedicated to Richard Guy on his 80th birthday, for all the inspiring problems that he has posed Contents 1 Introduction: Deenitions and properties of the spectrum 2 The natural and logarithmic densities of m-th power residues 2a The proportion of m-th power residues up to x 2b Logarithmic proportions of m-th power residues 3 Basic properties of integral equations 3a Existence and uniqueness of solutions and rst estimates 3b Inclusion-Exclusion inequalities 4 Proof of the Structure Theorem 4a Variation of averages of multiplicative functions 4b Some useful identities 4c Removing the impact of small primes 4d The Structure Theorem and Propositions 1 5 The spectrum of ?1; 1] 5a Preliminaries 5b Bounding
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تاریخ انتشار 2007