In this minicourse we discuss some old results concerning the location of zeros of partition functions (or moment generating functions) in certain statistical mechanics models and their possible connections to the Riemann Hypothesis (RH). A standard reformulation of the RH is as follows. The (two-sided) Laplace transform of a certain specific function \Psi on the real line is automatically an entire function on the complex plane; the RH is equivalent to this transform having only pure imaginary zeros. Also
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