Density of the union of positive diagonal binary quadratic forms

Diao, Yijie

Density of the union of positive diagonal binary quadratic forms

Diao Y. 2023. Density of the union of positive diagonal binary quadratic forms. Acta Arithmetica. 207, 1–17.

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https://doi.org/10.48550/arXiv.2103.08268 [Preprint]

DOI

10.4064/aa210830-24-11

Journal Article | Published | English

Author

Diao, Yijie^ISTA

Department

Graduate School

Abstract

Let X be a sufficiently large positive integer. We prove that one may choose a subset S of primes with cardinality O(logX) such that a positive proportion of integers less than X can be represented by x2+py2 for at least one p∈S.

Keywords

Algebra; Number Theory

Publishing Year

2023

Date Published

2023-01-09

Journal Title

Acta Arithmetica

Publisher

Instytut Matematyczny

Acknowledgement

This article is a version the author’s master thesis at the University of Bonn. The author would like to thank his advisor Valentin Blomer for introducing the problem, and giving generous feedback and encouragement along the way, especially during the global pandemic. The author thanks Edgar Assing for his lectures on analytic number theory. Finally, the author is grateful to the anonymous referees for their valuable time and comments.

Volume

207

Page

1-17

ISSN

0065-1036

eISSN

1730-6264

IST-REx-ID

12406

Cite this

Diao Y. Density of the union of positive diagonal binary quadratic forms. Acta Arithmetica. 2023;207:1-17. doi:10.4064/aa210830-24-11

Diao, Y. (2023). Density of the union of positive diagonal binary quadratic forms. Acta Arithmetica. Instytut Matematyczny. https://doi.org/10.4064/aa210830-24-11

Diao, Yijie. “Density of the Union of Positive Diagonal Binary Quadratic Forms.” Acta Arithmetica. Instytut Matematyczny, 2023. https://doi.org/10.4064/aa210830-24-11.

Y. Diao, “Density of the union of positive diagonal binary quadratic forms,” Acta Arithmetica, vol. 207. Instytut Matematyczny, pp. 1–17, 2023.

Diao Y. 2023. Density of the union of positive diagonal binary quadratic forms. Acta Arithmetica. 207, 1–17.

Diao, Yijie. “Density of the Union of Positive Diagonal Binary Quadratic Forms.” Acta Arithmetica, vol. 207, Instytut Matematyczny, 2023, pp. 1–17, doi:10.4064/aa210830-24-11.

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