Estimates for Smooth Weyl Sums on Major Arcs
Abstract We present estimates for smooth Weyl sums of use on sets of major arcs in applications of the Hardy–Littlewood method. In particular, we derive mean value estimates on major arcs for smooth Weyl sums of degree $k$ delivering essentially optimal bounds for moments of order $u$ whenever $u>2\lfloor k/2\rfloor +4$.
Authors
- Jörg Brüdern (ORCID: https://orcid.org/0000-0003-0354-3644)
- Trevor D. Wooley (ORCID: https://orcid.org/0000-0002-8781-4706)
Institutions
- Purdue University West Lafayette (US)
- University of Göttingen (DE)
Publication Details
- Journal
- International Mathematics Research Notices
- Published
- 2024-11-26
- DOI
- https://doi.org/10.1093/imrn/rnae252
- Citations
- 1
- Primary Topic
- Analytic Number Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 1.27