Search Results for ""

Landau (1911) proved that for any fixed x>1, sum_(0<|I[rho]|<=T)x^rho=-T/(2pi)Lambda(x)+O(lnT) as T->infty, where the sum runs over the nontrivial Riemann zeta function zeros ...

The prime signature of a positive integer n is a sorted list of nonzero exponents a_i in the prime factorization n=p_1^(a_1)p_2^(a_2).... By definition, the prime signature ...

A prime number (or prime integer, often simply called a "prime" for short) is a positive integer p>1 that has no positive integer divisors other than 1 and p itself. More ...

The distinct prime factors of a positive integer n>=2 are defined as the omega(n) numbers p_1, ..., p_(omega(n)) in the prime factorization ...

Two integers are relatively prime if they share no common positive factors (divisors) except 1. Using the notation (m,n) to denote the greatest common divisor, two integers m ...

There are two types of functions known as Hankel functions. The more common one is a complex function (also called a Bessel function of the third kind, or Weber Function) ...

Given a sequence {a_n}_(n=1)^infty, a formal power series f(s) = sum_(n=1)^(infty)(a_n)/(n^s) (1) = a_1+(a_2)/(2^s)+(a_3)/(3^s)+... (2) is called the Dirichlet generating ...

An additive function is an arithmetic function such that whenever positive integers a and b are relatively prime, f(ab)=f(a)+f(b). An example of an additive function is ...

A prime constellation, also called a prime k-tuple, prime k-tuplet, or prime cluster, is a sequence of k consecutive numbers such that the difference between the first and ...

A function f(m) is called multiplicative if (m,m^')=1 (i.e., the statement that m and m^' are relatively prime) implies f(mm^')=f(m)f(m^') (Wilf 1994, p. 58). Examples of ...