Special cubic zeros and the dual variety

Wang, Victor

Special cubic zeros and the dual variety

Wang V. 2024. Special cubic zeros and the dual variety. Journal of the London Mathematical Society. 110(3), e12975.

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DOI

10.1112/jlms.12975

Journal Article | Published | English

Scopus indexed

Author

Wang, Victor^ISTA

Corresponding author has ISTA affiliation

Department

Browning Group

Grant

IST-BRIDGE: International postdoctoral program

Abstract

Let F be a diagonal cubic form over Z in six variables. From the dual variety in the delta method of Duke–Friedlander–Iwaniec and Heath‐Brown, we unconditionally extract a weighted count of certain special integral zeros of F in regions of diameter X - 8 . Heath‐Brown did the same in four variables, but our analysis differs and captures some novel features. We also put forth an axiomatic framework for more general F.

Publishing Year

2024

Date Published

2024-08-14

Journal Title

Journal of the London Mathematical Society

Publisher

Wiley

Acknowledgement

This paper is an important component of the thesis work described in [25]; many of my acknowledgements there apply here as well. I also thank my advisor, Peter Sarnak, for many helpful suggestions and questions on the exposition, references, assumptions, and scope of (various drafts of) the present work. I am also grateful to Trevor Wooley for providing some helpful general comments on special subvarieties and the reference [24]. I thank Tim Browning for inspiring part of the current title of the paper. Finally, thanks are due to the referee for providing many helpful suggestions. This work was partially supported by NSF grant DMS-1802211, and the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant AgreementNo. 101034413.

Volume

110

Issue

Article Number

e12975

ISSN

0024-6107

eISSN

1469-7750

IST-REx-ID

17447

Cite this

Wang V. Special cubic zeros and the dual variety. Journal of the London Mathematical Society. 2024;110(3). doi:10.1112/jlms.12975

Wang, V. (2024). Special cubic zeros and the dual variety. Journal of the London Mathematical Society. Wiley. https://doi.org/10.1112/jlms.12975

Wang, Victor. “Special Cubic Zeros and the Dual Variety.” Journal of the London Mathematical Society. Wiley, 2024. https://doi.org/10.1112/jlms.12975.

V. Wang, “Special cubic zeros and the dual variety,” Journal of the London Mathematical Society, vol. 110, no. 3. Wiley, 2024.

Wang V. 2024. Special cubic zeros and the dual variety. Journal of the London Mathematical Society. 110(3), e12975.

Wang, Victor. “Special Cubic Zeros and the Dual Variety.” Journal of the London Mathematical Society, vol. 110, no. 3, e12975, Wiley, 2024, doi:10.1112/jlms.12975.

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