The Davenport–Heilbronn method: 80 years on

Browning, Timothy D

The Davenport–Heilbronn method: 80 years on

Browning TD. 2026. The Davenport–Heilbronn method: 80 years on. Journal of the London Mathematical Society. 113(1), e70371.

Download

2026_JourLondonMathSoc_Browning.pdf 235.24 KB [Published Version]

DOI

10.1112/jlms.70371

Journal Article | Published | English

Scopus indexed

Author

Browning, Timothy D^ISTA

Corresponding author has ISTA affiliation

Department

Browning Group

Grant

Rational curves via function field analytic number theory

Abstract

The Davenport–Heilbronn method is a version of the circle method that was developed for studying Diophantine inequalities in the paper (Davenport and Heilbronn, J. Lond. Math. Soc. (1) 21 (1946), 185–193). We discuss the main ideas in the paper, together with an account of the development of the subject in the intervening 80 years.

Publishing Year

2026

Date Published

2026-01-06

Journal Title

Journal of the London Mathematical Society

Publisher

Wiley

Acknowledgement

The author is very grateful to Jörg Brüdern, Simon Rydin Myerson and Trevor Wooley for their help and advice with preparing this survey, in addition to Vinay Kumaraswamy, Victor Wang and the anonymous referee for useful comments on an earlier draft. This work was supported by a FWF Grant (DOI 10.55776/P36278). Open Access funding provided by Institute of Science and Technology Austria/KEMÖ.

Volume

113

Issue

Article Number

e70371

ISSN

0024-6107

eISSN

1469-7750

IST-REx-ID

21002

Cite this

Browning TD. The Davenport–Heilbronn method: 80 years on. Journal of the London Mathematical Society. 2026;113(1). doi:10.1112/jlms.70371

Browning, T. D. (2026). The Davenport–Heilbronn method: 80 years on. Journal of the London Mathematical Society. Wiley. https://doi.org/10.1112/jlms.70371

Browning, Timothy D. “The Davenport–Heilbronn Method: 80 Years On.” Journal of the London Mathematical Society. Wiley, 2026. https://doi.org/10.1112/jlms.70371.

T. D. Browning, “The Davenport–Heilbronn method: 80 years on,” Journal of the London Mathematical Society, vol. 113, no. 1. Wiley, 2026.

Browning TD. 2026. The Davenport–Heilbronn method: 80 years on. Journal of the London Mathematical Society. 113(1), e70371.

Browning, Timothy D. “The Davenport–Heilbronn Method: 80 Years On.” Journal of the London Mathematical Society, vol. 113, no. 1, e70371, Wiley, 2026, doi:10.1112/jlms.70371.

All files available under the following license(s):

Creative Commons Attribution 4.0 International Public License (CC-BY 4.0):