Dirichlet Multiplication : Number Theory #Dirichlet #Multiplication #: #Number #Theory
The Dirichlet product of arithmetical functions : Definition : If f and g are two arithmetical functions then we define their Dirichlet product ( or Dirichlet convolution ) to be the arithmetical function f *g defined by the equation (f * g)(n) = 𝜮 f(d) g(n/d) for d/n Notation : The symbol N will be used for the arithmetical function for which N(n) = n ∀ n. From this notation , we can relate the Mobius function ( 𝝁 ) and Euler totient function ( Ჶ ) by Ჶ = 𝝁 * N. Note : The Concept Dirichlet multiplication helps clarify interrelations between various arithmetical functions. Result : Dirichlet multiplication is commuta...