We define the Liouville function X(n) by setting X(1) = 1 . If n > 1, we consider the prime power factorization n = p1•p. . · pm and define A(n) = (-1)ª1+az++am * Pm and ... (a) Prove that X is multiplicative. (b) Prove that the summatory function of X, A(n) = Edn^(d) is multiplicative.
We define the Liouville function X(n) by setting X(1) = 1 . If n > 1, we consider the prime power factorization n = p1•p. . · pm and define A(n) = (-1)ª1+az++am * Pm and ... (a) Prove that X is multiplicative. (b) Prove that the summatory function of X, A(n) = Edn^(d) is multiplicative.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:We define the Liouville function X(n) by setting A(1) = 1. If n > 1,
we consider the prime power factorization n = p" · p,
P - P Pm and
..
define A(n) = (-1)ª1+a2+.·+am
(a) Prove that is multiplicative.
(b) Prove that the summatory function of A, A(n) = Edn^(d) is
multiplicative.
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