Asymptotic growth of translation-dilation orbits

Abstract

By studying some Clausen-like multiple Dirichlet series, we complete the proof of Manin's conjecture for sufficiently split smooth equivariant compactifications of the translation-dilation group over the rationals. Secondary terms remain elusive in general.

52 pages; final version

References in corpus (7)

• Distribution of periodic torus orbits and Duke's theorem for cubic fields
• Manin's conjecture for toric varieties
• Rational points on compactifications of semi-simple algebraic groups
• Secondary terms in asymptotics for the number of zeros of quadratic forms over number fields
• Counting imaginary quadratic points via universal torsors, II
• The distribution of $S$-integral points on ${\mathrm{SL}}_2$-orbit closures of binary forms
• Special cubic zeros and the dual variety