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arXiv · 1707.04801

Asymptotic formula of the number of Newton polygons

Shushi Harashita
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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.

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Shushi Harashita. 2020-03-25. Asymptotic formula of the number of Newton polygons. https://doi.org/10.1007/s00209-020-02504-w

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