This chapter may be viewed as an extension of the previous one, in the sense that multiplicative functions may generalize Euclid’s fundamental theorem of integer factorizations. The text is aimed at introducing the Dirichlet convolution product, thus giving a ring structure to the set of arithmetic functions, and then establishing some useful summation results for multiplicative functions with the help of the Möbius inversion formula. The section Further Developments is devoted to a complete study of Dirichlet series from an arithmetic viewpoint and we also provide some estimates for other types of summation, such as multiplicative functions over short intervals or additive functions. Finally, a brief account of Selberg’s sieve and the large sieve is also given.
KeywordsAsymptotic Formula Dirichlet Series Inversion Formula Multiplicative Function Average Order
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