Product of Sets on Varieties in Finite Fields

Let V be a variety in F q d and E ⊂ V . It is known that if any line passing through the origin contains a bounded number of points from E , then ∏ ( E ) = | { x · y : x , y ∈ E } | ≫ q whenever | E | ≫ q d 2 . In this paper, we show that the barrier d 2 can be broken when V is a paraboloid in some...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:The Journal of fourier analysis and applications 2024-04, Vol.30 (2), Article 19
Hauptverfasser: Chang, Che-Jui, Mohammadi, Ali, Pham, Thang, Shen, Chun-Yen
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:Let V be a variety in F q d and E ⊂ V . It is known that if any line passing through the origin contains a bounded number of points from E , then ∏ ( E ) = | { x · y : x , y ∈ E } | ≫ q whenever | E | ≫ q d 2 . In this paper, we show that the barrier d 2 can be broken when V is a paraboloid in some specific dimensions. The main novelty in our approach is to link this question to the distance problem in one lower dimensional vector space, allowing us to use recent developments in this area to obtain improvements.
ISSN:1069-5869
1531-5851
DOI:10.1007/s00041-024-10079-x