 96115 Contucci P., Knauf A.
 The Low Activity Phase of Some Dirichlet Series
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Apr 1, 96

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Abstract. We show that a rigorous statistical mechanics description of some
Dirichlet series is possible.
Using the abstract polymer model language of statistical mechanics
and the polymer expansion theory we characterize the low activity
phase by the suitable exponential decay of the truncated correlation
functions.
The result is obtained with a finitevolume approximation of the
Dirichlet series which turns out to be the gran canonical partition
function of a hardcore interacting system.
The correlation functions, which have a deep number theoretical
meaning being the probability of suitable divisibility properties,
are controlled, in the thermodynamical limit, by means of the
KirkwoodSalsburg type iterative equations.
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