On asymptotic estimates for arithmetic cost functions
نویسندگان
چکیده
منابع مشابه
Asymptotic properties of functions defined on arithmetic semigroups
Asymptotic properties of certain special arithmetical functions, like the divisor function τ(n), the sum-of-divisors function σ(n) and the Euler function φ(n) can be investigated in the general setting of arithmetical semigroups. The book of J. Knopfmacher [8] contains a detailed study of such properties, including asymptotic formulae with error estimates and extremal orders of magnitude of fun...
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Let f (m, n) denote the number of relatively prime subsets of {m+ 1, m + 2,. .. , n}, and let Φ(m, n) denote the number of subsets A of {m + 1, m + 2,. .. , n} such that gcd(A) is relatively prime to n. Let f k (m, n) and Φ k (m, n) be the analogous counting functions restricted to sets of cardinality k. Simple explicit formulas and asymptotic estimates are obtained for these four functions. A ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1997
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-97-03583-1