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math.NT2026
A note on Bremner's conjecture and uniformity
Natalia Garcia-Fritz, Hector Pasten
In 1998, Bremner conjectured that elliptic curves over the rationals having long sequences of distinct rational points whose -coordinates are in arithmetic progression, have lar…
math.NT2026
Patterns on elliptic curves beyond Bremner's conjecture
Natalia Garcia-Fritz, Hector Pasten
In the late 1990's, Bremner conjectured that long arithmetic progressions among the -coordinates of rational points of an elliptic curve over should force the r…
math.NT2026
Towards Lang--Vojta via Degeneration
Ryan C. Chen, Natalia Garcia-Fritz, Siddharth Mathur +1
Towards the Lang--Vojta conjecture, we prove results on finiteness and Zariski degeneracy of -integral points of varieties over number fields , including many cases with geom…