Arithmetic Functions and Integer Products - P. D. T. A. Elliott

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Sommaire:
Duality and the Differences of Additive Functions.- First Motive.- 1 Variants of Well-Known Arithmetic Inequalities.- 2 A Diophantine Equation.- 3 A First Upper Bound.- 4 Intermezzo: The Group Q*/?.- 5 Some Duality.- Second Motive.- 6 Lemmas Involving Prime Numbers.- 7 Additive Functions on Arithmetic Progressions with Large Moduli.- 8 The Loop.- Third Motive.- 9 The Approximate Functional Equation.- 10 Additive Arithmetic Functions on Differences.- 11 Some Historical Remarks.- 12 From L2 to L?.- 13 A Problem of K?tai.- 14 Inequalities in L?.- 15 Integers as Products.- 16 The Second Intermezzo.- 17 Product Representations by Values of Rational Functions.- 18 Simultaneous Product Representations by Values of Rational Functions.- 19 Simultaneous Product Representations with aix + bi.- 20 Information and Arithmetic.- 21 Central Limit Theorem for Differences.- 22 Density Theorems.- 23 Problems.- Supplement Progress in Probabilistic Number Theory.- References.