1 December 2010
Journal of Mathematical Sciences
Subject to the abc-conjecture, we improve the standard Weyl estimate for cubic exponential sums in which the argument is a quadratic irrational. Specifically. we show that, for any ε > 0 and any quadratic irrational α ∈ ℝ-ℚ. Classically one would have had the (unconditional) exponent 3/4 + ε for such α. Bibliography: 5 titles. © 2010 Springer Science+Business Media, Inc.
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