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

Average sizes of mixed character sums
V. Wang, M. Xu, Proceedings of the Royal Society of Edinburgh: Section A Mathematics (2026) 1–15.

Integral solutions to systems of diagonal equations
N. Rome, S. Yamagishi, Pacific Journal of Mathematics 340 (2026) 179–198.

Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve
S. Baraczuk, B. Naskrcki, M. Verzobio, Journal of Number Theory 279 (2026) 170–183.

Common valuations of division polynomials
B. Naskrcki, M. Verzobio, Proceedings of the Royal Society of Edinburgh Section A: Mathematics 155 (2025) 1646–1660.

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

Class numbers and integer points on some Pellian surfaces
Y. Diao, Journal de Theorie Des Nombres de Bordeaux 37 (2025) 973–988.

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

Quartic polynomials in two variables do not represent all non-negative integers
S. Yao Xiao, S. Yamagishi, 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.

On a question of Davenport and diagonal cubic forms over Fq(t)
J. Glas, L. Hochfilzer, Mathematische Annalen 391 (2025) 5485–5533.

Diagonal cubic forms and the large sieve
V. Wang, Mathematika 71 (2025).

Birch’s theorem on forms in many variables with a Hessian condition
S. Yamagishi, Acta Arithmetica 221 (2025) 141–151.

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

Harper’s beyond square-root conjecture
V. Wang, M.W. Xu, International Mathematics Research Notices 2025 (2025).

Motivic distribution of rational curves and twisted products of toric varieties
L. Faisant, Algebra &; Number Theory 19 (2025) 883–965.

Averages of multiplicative functions along equidistributed sequences
S. Chan, P. Koymans, C. Pagano, E. Sofos, Journal of Number Theory 273 (2025) 1–36.

Motivic counting of rational curves with tangency conditions via universal torsors
L. Faisant, ArXiv (n.d.).

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

Asymptotic growth of translation-dilation orbits
V. Wang, Advances in Mathematics 475 (2025).