Von Mangoldt function Essay Example | Topics and Well Written Essays - 1250 words

Von Mangoldt function - Essay Example There are various functions that relates to the Von function. Some of the functions that relates to the Von function is the mobius function, the divisor function and the phi function amongst others. In number theory, the phi function φ(n), is a part of the arithmetic function that counts the n totatives, that is, the positive integers that are less than or equal to n that are mainly prime to n. If n is a positive integer, then φ(n) is the integer number k in the range 1 ≠¤ k ≠¤ n for which the biggest common divisor gcd (n,k)=1. The totient function refers to a multiplicative function that means that where two numbers n and m are relatively prim, then φ(mn)  =  Ãâ€ (m)φ(n). The Euler’s product formula states A divisor function is also a part of the arithmetic function linked to the integer divisors. When denoted as the divisor function, it states the integer divisors number. It comes out as a remarkable identities involving relationships with the Eisenstein series and Riemann zeta function of modular forms. A linked formula is the divisor summatory function that like the name is the sum exceeding the divisor function. The Von function is related to the divisor function through the summatory function. The subsequent chebyshey function ψ(x) is the summatory function associated with the von Mangoldt function: There are various aspects that surround the Von function. Many questions have been asked as to whether the Von function is multiplicative. The von function is one of the most significant arithmetic function that cannot be classified as additive or multiplicative. An arithmetic function a is said to be completely additive if a (mn) = a (m) + a (n) for all the natural numbers m and n. An arithmetic function is attributed to be completely multiplicative if a (mn) = a (m) a (n) for all the natural numbers m and n. Two whole numbers n and m are referred to as comprise if their greatest common divisor equals 1, meaning that there