Show that if f and g are multiplicative functions, then the Dirichlet product f g, defined by (f g)(n):=Egn f(d)g(n/d), is also multiplicative.
Show that if f and g are multiplicative functions, then the Dirichlet product f g, defined by (f g)(n):=Egn f(d)g(n/d), is also 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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Show that if f and g are multiplicative functions, then the Dirichlet
product f • g, defined by (f g)(n):= Edn F(d)g(n/d), is also multiplicative.
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