# Accession Number:

## AD0661238

# Title:

## THEOREMS ABOUT BEURLING'S GENERALIZED PRIMES AND THE ASSOCIATED ZETA FUNCTION.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## ILLINOIS UNIV URBANA

# Personal Author(s):

# Report Date:

## 1967-06-01

# Pagination or Media Count:

## 77.0

# Abstract:

Beurling defined a set, P, of generalized prime numbers as any non-decreasing unbounded sequence of real numbers which are greater than one. The multiplicative semi-group, N, generated by the elements of P is called the associated set of generalized integers. The functions Pi x and N x are defined, respectively, as the number of generalized prime and integers less than or equal to x. This paper is concerned with deducing the behaviour of Pi x from that of N x.

# Descriptors:

# Subject Categories:

- Statistics and Probability