Beurling zeta function
In mathematics, a Beurling zeta function is an analogue of the Riemann zeta function where the ordinary primes are replaced by a set of Beurling generalized primes: any sequence of real numbers greater than 1 that tend to infinity. These were introduced by.
A Beurling generalized integer is a number that can be written as a product of Beurling generalized primes. Beurling generalized the usual prime number theorem to Beurling generalized primes. He showed that if the number N of Beurling generalized integers less than x is of the form N = Ax + O with γ > 3/2 then the number of Beurling generalized primes less than x is asymptotic to x/log x, just as for ordinary primes,
but if γ = 3/2 then this conclusion need not hold.
