Bounds for the Cubic Weyl Sum
classification
🧮 math.NT
keywords
alphaepsilonabc-conjectureboundscubicirrationalquadraticsubject
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It is shown, subject to the abc-conjecture, that \[\sum_{n\le N}\exp(2\pi i\alpha n^3)\ll_{\epsilon,\alpha}N^{5/7+\epsilon}\] for any $\epsilon>0$ and any quadratic irrational $\alpha$.
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