Counting numbers in multiplicative sets: Landau versus Ramanujan

Details Counting numbers in multiplicative sets: Landau versus Ramanujan Counting numbers in multiplicative sets: Landau versus Ramanujan

2011-10-04

arxiv.org/abs/1110.0708v1

Mathematics

Number Theory

15 pages, 1 Table

Scientific paper

A set S of integers is said to be multiplicative if for every pair m and n of coprime integers we have that mn is in S iff both m and n are in S. Both Landau and Ramanujan gave approximations to S(x), the number of n<=x that are in S, for specific choices of S. The asymptotical precision of their respective approaches are being compared and related to Euler-Kronecker constants, a generalization of Euler's constant gamma=0.57721566.... This paper claims little originality, its aim is to give a survey on the literature related to this theme with an emphasis on the contributions of the author (and his coauthors).

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