Arithmetic of higher-dimensional orbifolds and a mixed Waring problem

Browning TD, Yamagishi S. 2021. Arithmetic of higher-dimensional orbifolds and a mixed Waring problem. Mathematische Zeitschrift. 299, 1071–1101.

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Author
Browning, Timothy DIST Austria ; Yamagishi, Shuntaro
Department
Abstract
We study the density of rational points on a higher-dimensional orbifold (Pn−1,Δ) when Δ is a Q-divisor involving hyperplanes. This allows us to address a question of Tanimoto about whether the set of rational points on such an orbifold constitutes a thin set. Our approach relies on the Hardy–Littlewood circle method to first study an asymptotic version of Waring’s problem for mixed powers. In doing so we make crucial use of the recent resolution of the main conjecture in Vinogradov’s mean value theorem, due to Bourgain–Demeter–Guth and Wooley.
Publishing Year
Date Published
2021-03-05
Journal Title
Mathematische Zeitschrift
Acknowledgement
While working on this paper the authors were both supported by EPSRC grant EP/P026710/1, and the second author received additional support from the NWO Veni Grant 016.Veni.192.047. Thanks are due to Marta Pieropan, Arne Smeets and Sho Tanimoto for useful conversations related to this topic, and to the anonymous referee for numerous helpful suggestions.
Volume
299
Page
1071–1101
ISSN
eISSN
IST-REx-ID

Cite this

Browning TD, Yamagishi S. Arithmetic of higher-dimensional orbifolds and a mixed Waring problem. Mathematische Zeitschrift. 2021;299:1071–1101. doi:10.1007/s00209-021-02695-w
Browning, T. D., & Yamagishi, S. (2021). Arithmetic of higher-dimensional orbifolds and a mixed Waring problem. Mathematische Zeitschrift. Springer Nature. https://doi.org/10.1007/s00209-021-02695-w
Browning, Timothy D, and Shuntaro Yamagishi. “Arithmetic of Higher-Dimensional Orbifolds and a Mixed Waring Problem.” Mathematische Zeitschrift. Springer Nature, 2021. https://doi.org/10.1007/s00209-021-02695-w.
T. D. Browning and S. Yamagishi, “Arithmetic of higher-dimensional orbifolds and a mixed Waring problem,” Mathematische Zeitschrift, vol. 299. Springer Nature, pp. 1071–1101, 2021.
Browning TD, Yamagishi S. 2021. Arithmetic of higher-dimensional orbifolds and a mixed Waring problem. Mathematische Zeitschrift. 299, 1071–1101.
Browning, Timothy D., and Shuntaro Yamagishi. “Arithmetic of Higher-Dimensional Orbifolds and a Mixed Waring Problem.” Mathematische Zeitschrift, vol. 299, Springer Nature, 2021, pp. 1071–1101, doi:10.1007/s00209-021-02695-w.
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