Article
Licensed
Unlicensed
Requires Authentication
On the fourth derivative test for exponential sums
-
Olivier Robert
Published/Copyright:
May 21, 2015
Abstract
We give an upper bound for the exponential sum ∑m=1,...,M exp(2iπf(m)) where f is a real-valued function whose fourth derivative has the order of magnitude λ > 0 small. Van der Corput's classical bound, in terms of M and λ only, involves the exponent 1/14. We show how this exponent may be replaced by any θ < 1/12 without further hypotheses. The proof uses a recent result by Wooley on the cubic Vinogradov system.
Keywords: Exponential sums; Vinogradov system
MSC: 11L07
Received: 2014-12-12
Published Online: 2015-5-21
Published in Print: 2016-3-1
© 2016 by De Gruyter
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- Frontmatter
- Ring class invariants over imaginary quadratic fields
- The structure of p-local compact groups of rank 1
- Sampling and interpolation on some nilpotent Lie groups
- Topology of moduli spaces of free group representations in real reductive groups
- Finite symmetries of S4
- Variations of Minkowski's theorem on successive minima
- A one-relator group with long lower central series
- On transfinite nilpotence of the Vogel–Levine localization
- Time inhomogeneous generalized Mehler semigroups and skew convolution equations
- Specifying the Auslander–Reiten translation for complexes of modules
- Second order elliptic operators with diffusion coefficients growing as |x|α at infinity
- On the fourth derivative test for exponential sums
Articles in the same Issue
- Frontmatter
- Ring class invariants over imaginary quadratic fields
- The structure of p-local compact groups of rank 1
- Sampling and interpolation on some nilpotent Lie groups
- Topology of moduli spaces of free group representations in real reductive groups
- Finite symmetries of S4
- Variations of Minkowski's theorem on successive minima
- A one-relator group with long lower central series
- On transfinite nilpotence of the Vogel–Levine localization
- Time inhomogeneous generalized Mehler semigroups and skew convolution equations
- Specifying the Auslander–Reiten translation for complexes of modules
- Second order elliptic operators with diffusion coefficients growing as |x|α at infinity
- On the fourth derivative test for exponential sums
