A new kth derivative estimate for exponential sums via Vinogradov’s mean value
- Авторлар: Heath-Brown D.R.1
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Мекемелер:
- Mathematical Institute
- Шығарылым: Том 296, № 1 (2017)
- Беттер: 88-103
- Бөлім: Article
- URL: https://journals.rcsi.science/0081-5438/article/view/174203
- DOI: https://doi.org/10.1134/S0081543817010072
- ID: 174203
Дәйексөз келтіру
Аннотация
We give a slight refinement to the process by which estimates for exponential sums are extracted from bounds for Vinogradov’s mean value. Coupling this with the recent works of Wooley, and of Bourgain, Demeter and Guth, providing optimal bounds for the Vinogradov mean value, we produce a powerful new kth derivative estimate. Roughly speaking, this improves the van der Corput estimate for k ≥ 4. Various corollaries are given, showing for example that \(\zeta \left( {\sigma + it} \right){ \ll _\varepsilon }{t^{{{\left( {1 - \sigma } \right)}^{3/2}}/2 + \varepsilon }}\) for t ≥ 2 and 0 ≤ σ ≤ 1, for any fixed ε > 0.
Авторлар туралы
D. Heath-Brown
Mathematical Institute
Хат алмасуға жауапты Автор.
Email: rhb@maths.ox.ac.uk
Ұлыбритания, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG
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