1. CJM 2009 (vol 61 pp. 465)
 Woodford, Roger

On Partitions into Powers of Primes and Their Difference Functions
In this paper, we extend the approach first outlined by Hardy and
Ramanujan for calculating the asymptotic formulae for the number of
partitions into $r$th powers of primes, $p_{\mathbb{P}^{(r)}}(n)$,
to include their difference functions. In doing so, we rectify an
oversight of said authors, namely that the first difference function
is perforce positive for all values of $n$, and include the
magnitude of the error term.
Categories:05A17, 11P81 

2. CJM 1997 (vol 49 pp. 641)
 Burris, Stanley; Compton, Kevin; Odlyzko, Andrew; Richmond, Bruce

Fine spectra and limit laws II Firstorder 01 laws.
Using FefermanVaught techniques a condition on the fine
spectrum of an admissible class of structures is found
which leads to a firstorder 01 law.
The condition presented is best possible in the
sense that if it is violated then one can find an admissible
class with the same fine spectrum which does not have
a firstorder 01 law.
If the condition is satisfied (and hence we have a firstorder %% 01 law)
Categories:03N45, 11N45, 11N80, 05A15, 05A16, 11M41, 11P81 

3. CJM 1997 (vol 49 pp. 468)
 Burris, Stanley; Sárközy, András

Fine spectra and limit laws I. Firstorder laws
Using FefermanVaught techniques we show a certain property of the fine
spectrum of an admissible class of structures leads to a firstorder law.
The condition presented is best possible in the sense that if it is
violated then one can find an admissible class with the same fine
spectrum which does not have a firstorder law. We present three
conditions for verifying that the above property actually holds.
The first condition is that the count function of an admissible class
has regular variation with a certain uniformity of convergence. This
applies to a wide range of admissible classes, including those
satisfying Knopfmacher's Axiom A, and those satisfying Bateman
and Diamond's condition.
The second condition is similar to the first condition, but designed
to handle the discrete case, {\it i.e.}, when the sizes of the structures
in an admissible class $K$ are all powers of a single integer. It applies
when either the class of indecomposables or the whole class satisfies
Knopfmacher's Axiom A$^\#$.
The third condition is also for the discrete case, when there is a
uniform bound on the number of $K$indecomposables of any given size.
Keywords:First order limit laws, generalized number theory Categories:O3C13, 11N45, 11N80, 05A15, 05A16, 11M41, 11P81 
