Asymptotic prime partitions of integers

URN to cite this document:: urn:nbn:de:bvb:355-epub-390076
DOI to cite this document:: 10.5283/epub.39007

Bartel, Johann ; Bhaduri, R. K. ; Brack, Matthias ; Murthy, M. V. N.

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Date of publication of this fulltext: 20 Mar 2019 12:56

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Abstract

In this paper, we discuss P(n), the number of ways a given integer n may be written as a sum of primes. In particular, an asymptotic form P-as(n) valid for n ->infinity is obtained analytically using standard techniques of quantum statistical mechanics. First, the bosonic partition function of primes, or the generating function of unrestricted prime partitions in number theory, is constructed. ...