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

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).

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1967
Accession Number
AD0661238

Entities

People

  • Richard S. Hall

Organizations

  • University of Illinois Urbana–Champaign

Tags

DTIC Thesaurus Topics

  • Mathematics
  • Numbers
  • Prime Numbers
  • Rational Numbers
  • Real Numbers
  • Sequences

Fields of Study

  • Mathematics

Readers

  • Linear Algebra