Abstract
From Mason's theorem on rational function fields (the progenitor of the abc-conjecture) we immediately derive upper bounds for “syzygy gaps” (Theorems 3, 8, 11, and Corollary 9). These in turn quickly give: (1) The author's conjecture Z ( l ) , used in the study of Hilbert–Kunz series. (2) A lower bound for certain “ F-pure thresholds.” (3) Han's explicit description of the 3-dimensional p-fractal attached to x, y and x + y . (4) Some apparently simple degree estimates, observed in the past but unproved until now (Corollary 6 and Theorem 10).
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