The founders of the theory were Paul Erdős, Aurel Wintner and Mark Kac during the 1930s, one of the periods of investigation in analytic number theory.
Aurel Wintner, mathematician; one of the founders of probabilistic number theory
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At the University of Leipzig he founded a mathematical school and his students, including Ernst Hölder, Erich Kähler, Aurel Wintner, Hermann Boerner and Karl Maruhn, continuing his research in mathematics and theoretical physics.