Title: Asymptotic formula of the number of Newton polygons,
Abstract: In this paper, we enumerate Newton polygons asymptotically. The number of
Newton polygons is computable by a simple recurrence equation, but unexpectedly
the asymptotic formula of its logarithm contains growing oscillatory terms. As
the terms come from non-trivial zeros of the Riemann zeta function, an
estimation of the amplitude of the oscillating part is equivalent to the
Riemann hypothesis.