Bounds for the cubic Weyl sum
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...
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| Médium: | Journal article |
| Jazyk: | English |
| Vydáno: |
2010
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| Shrnutí: | 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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