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

Integral points on cubic surfaces: heuristics and numerics
T.D. Browning, F.A. Wilsch, Selecta Mathematica New Series 31 (2025).

Pairs of commuting integer matrices
T.D. Browning, W. Sawin, V. Wang, Mathematische Annalen 393 (2025) 1863–1880.

Optimal sums of three cubes in Fq[t]
T.D. Browning, J. Glas, V. Wang, Mathematische Zeitschrift 310 (2025).

Counting integer points on affine surfaces with a side condition
T.D. Browning, M. Verzobio, Discrete Analysis 2025 (2025).

Paucity of rational points on fibrations with multiple fibres
T.D. Browning, J. Lyczak, A. Smeets, Algebra &; Number Theory 19 (2025) 2049–2090.

Almost all quadratic twists of an elliptic curve have no integral points
T.D. Browning, S. Chan, Journal of the European Mathematical Society (2025).

Solubility of a resultant equation and applications
T.D. Browning, S. Chan, Journal de l’ecole Polytechnique Mathematiques 12 (2025) 1677–1691.

The polynomial sieve and equal sums of like polynomials
T.D. Browning, International Mathematics Research Notices 2024 (2024) 10165–10168.

Square-free values of random polynomials
T.D. Browning, I.E. Shparlinski, Journal of Number Theory 261 (2024) 220–240.

Density of rational points on some quadric bundle threefolds
D. Bonolis, T.D. Browning, Z. Huang, Mathematische Annalen 390 (2024) 4123–4207.

Generalised quadratic forms over totally real number fields
T.D. Browning, L.B. Pierce, D. Schindler, Journal of the Institute of Mathematics of Jussieu 23 (2024) 2859–2912.

Strong divisibility sequences and sieve methods
T.D. Browning, M. Verzobio, Mathematika 70 (2024).

Uniform bounds for rational points on hyperelliptic fibrations
D. Bonolis, T.D. Browning, Annali Della Scuola Normale Superiore Di Pisa - Classe Di Scienze 24 (2023) 173–204.

Free rational curves on low degree hypersurfaces and the circle method
T.D. Browning, W. Sawin, Algebra and Number Theory 17 (2023) 719–748.

Local solubility for a family of quadrics over a split quadric surface
T.D. Browning, J. Lyczak, R. Sarapin, Involve 16 (2023) 331–342.

The Hasse principle for random Fano hypersurfaces
T.D. Browning, P.L. Boudec, W. Sawin, Annals of Mathematics 197 (2023) 1115–1203.

Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5
T.D. Browning, New York Journal of Mathematics 28 (2022) 1193–1229.

Equidistribution and freeness on Grassmannians
T.D. Browning, T. Horesh, F.A. Wilsch, Algebra &; Number Theory 16 (2022) 2385–2407.

Cubic Forms and the Circle Method
T.D. Browning, Cubic Forms and the Circle Method, Springer Nature, Cham, 2021.