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

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

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

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

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

Counting rational points on smooth hypersurfaces with high degree
M. Verzobio, International Mathematics Research Notices 2025 (2025).

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.

On the existence of magic squares of powers
N. Rome, S. Yamagishi, Research in Number Theory 11 (2025).

Sumset growth in progression-free sets
C. Elsholtz, I.Z. Ruzsa, L. Wurzinger, Acta Arithmetica 220 (2025) 289–303.

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

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

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

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

6-torision and integral points on quartic threefolds
S. Chan, P. Koymans, C. Pagano, E. Sofos, Annali Della Scuola Normale Superiore Di Pisa, Classe Di Scienze (2025).

Prime Hasse principles via diophantine second moments
V. Wang, Journal of the Association for Mathematical Research 3 (2025) 1–26.

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

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

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).