Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the asymptotic prime partitions of integers   In this paper, we discuss P(n), the number of ways in which a given integer n
may be written as a sum of primes. In particular, an asymptotic form P_as(n)
valid for n towards 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. Next, the density of states is obtained using the
saddle-point method for Laplace inversion of the partition function in the
limit of large n. This directly gives the asymptotic number of prime partitions
P_as(n). The leading term in the asymptotic expression grows exponentially as
sqrt[n/ln(n)] and agrees with previous estimates. We calculate the
next-to-leading order term in the exponent, porportional to ln[ln(n)]/ln(n),
and show that an earlier result in the literature for its coefficient is
incorrect. Furthermore, we also calculate the next higher order correction,
proportional to 1/ln(n) and given in Eq.(43), which so far has not been
available in the literature. Finally, we compare our analytical results with
the exact numerical values of P(n) up to n \sim 8 10^6. For the highest values,
the remaining error between the exact P(n) and our P_as(n) is only about half
of that obtained with the leading-order (LO) approximation. But we also show
that, unlike for other types of partitions, the asymptotic limit for the prime
partitions is still quite far from being reached even for n \sim 10^7.

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The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg