Counting rational points on quartic del Pezzo surfaces with a rational conic

Abstract

Upper and lower bounds, of the expected order of magnitude, are obtained for the number of rational points of bounded height on any quartic del Pezzo surface over $\mathbb{Q}$ that contains a conic defined over $\mathbb{Q}$.

39 pages, to appear in Mathematische Annalen

References in corpus (2)

• Rational points of bounded height on general conic bundle surfaces
• Generalised divisor sums of binary forms over number fields

Cited by in corpus (1)

• On upper bounds of Manin type