2025/03/25 by Verzobio, Matteo · 1 citation
#11D41 #11D45 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2503.19451
Let X be a smooth projective hypersurface defined over ℚ. We provide new bounds for rational points of bounded height on X. In particular, we show that if X is a smooth projective hypersurface in ℙn with n≥ 4 and degree d≥ 50, then the set of rational points on X of height bounded by B have cardinality On,d,ε(Bn-2+ε). If X is smooth and has degree d≥ 6, we improve the dimension growth conjecture bound. We achieve an analogue result for affine hypersurfaces whose projective closure is smooth.