The Mangoldt Function ⴷ ( n ) : Number Theory #The #Mangoldt #Function #ⴷ ( n ) : #Number #Theory
Mangoldt Function : Definition For every n ≥ 1 we define ⴷ ( n ) = { log p if n = p m for some prime p and some m ≥ 1 = 0 Otherwise Since 1, 6, 10 can not be expressed as prime power , ⴷ( 0) = ⴷ(6) = ⴷ(10 ) = 0. For n = 2, we have 2 = 2 1 = P m , here m = 1 ∴ ⴷ ( 2 ) = log 2. For n = 3 , we have 3 = 3 1 = p m , here m = 1 ∴ ⴷ ( 3 ) = log 3 For n = 4, we have 4 = 2 2 = p m , here m = 2 ...