Bounds for the cubic Weyl sum

Author: 

Heath-Brown, D

Publication Date: 

1 December 2010

Journal: 

Journal of Mathematical Sciences

Last Updated: 

2019-06-16T03:32:06.177+01:00

Issue: 

6

Volume: 

171

DOI: 

10.1007/s10958-010-0184-7

page: 

813-823

abstract: 

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.

Symplectic id: 

149564

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article