Arithmetical functions : an introduction to elementary and analytic properties of arithmetic functions and to some of their almost-periodic properties

The Aim Of This Book Is To Characterize Certain Multiplicative And Additive Arithmetical Functions By Combining Methods From Number Theory With Some Simple Ideas From Functional And Harmonic Analysis. The Authors Achieve This Goal By Considering Convolutions Of Arithmetical Functions, Elementary Mean-value Theorems, And Properties Of Related Multiplicative Functions. They Also Prove The Mean-value Theorems Of Wirsing And Halász And Study The Pointwise Convergence Of The Ramanujan Expansion. Finally, Some Applications To Power Series With Multiplicative Coefficients Are Included, Along With Exercises And An Extensive Bibliography. Ch. I. Tools From Number Theory -- Ch. Ii. Mean-value Theorems And Multiplicative Functions, I -- Ch. Iii. Related Arithmetical Functions -- Ch. Iv. Uniformly Almost-periodic Arithmetical Functions -- Ch. V. Ramanujan Expansions Of Functions In B[superscript U] -- Ch. Vi. Almost-periodic And Almost-even Arithmetical Functions -- Ch. Vii. The Theorems Of Elliott And Daboussi -- Ch. Viii. Ramanujan Expansions -- Ch. Ix. Mean-value Theorems And Multiplicative Functions, Ii. Wolfgang Schwarz, Jürgen Spilker. Includes Bibliographical References (p. 333-352) And Indexes. Characterizes certain multiplicative and additive arithmetical functions by combining methods from number theory with simple ideas from functional and harmonic analysis