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Algebraic Geometry and Number TheoryAnalytic Number Theory ResearchAdvanced Combinatorial Mathematics

The Davenport–Heilbronn method: 80 years on

Tim Browning

2026.1.1JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES

DOI: 10.1112/jlms.70371

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.

Citation format

BROWNING, Tim. The davenport–heilbronn method: 80 years on. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2026, 113(1).