THEOREMS ABOUT BEURLING'S GENERALIZED PRIMES AND THE ASSOCIATED ZETA FUNCTION.
ILLINOIS UNIV URBANA
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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.
- Statistics and Probability