Asymptotic growth of translation-dilation orbits
Wang V. 2025. Asymptotic growth of translation-dilation orbits. Advances in Mathematics. 475, 110341.
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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.
Publishing Year
Date Published
2025-05-16
Journal Title
Advances in Mathematics
Publisher
Elsevier
Acknowledgement
I thank Yuri Tschinkel for introducing me to the beautiful paper [53] and associated open questions, and thank him as well as Ramin Takloo-Bighash and Sho Tanimoto for their encouragement and comments. Also, I thank Tim Browning and Dan Loughran for comments and suggestions concerning Manin–Peyre, homogeneous spaces, and splitness. Thanks also to Anshul Adve, Peter Sarnak, Philip Tosteson, Katy Woo, and Nina Zubrilina for some interesting discussions. I thank the Browning Group and Andy O'Desky for many conversations. This project has received funding from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 101034413. Finally, I thank the editors and referees for their detailed input, which substantially improved the paper.
Volume
475
Article Number
110341
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IST-REx-ID
Cite this
Wang V. Asymptotic growth of translation-dilation orbits. Advances in Mathematics. 2025;475. doi:10.1016/j.aim.2025.110341
Wang, V. (2025). Asymptotic growth of translation-dilation orbits. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2025.110341
Wang, Victor. “Asymptotic Growth of Translation-Dilation Orbits.” Advances in Mathematics. Elsevier, 2025. https://doi.org/10.1016/j.aim.2025.110341.
V. Wang, “Asymptotic growth of translation-dilation orbits,” Advances in Mathematics, vol. 475. Elsevier, 2025.
Wang V. 2025. Asymptotic growth of translation-dilation orbits. Advances in Mathematics. 475, 110341.
Wang, Victor. “Asymptotic Growth of Translation-Dilation Orbits.” Advances in Mathematics, vol. 475, 110341, Elsevier, 2025, doi:10.1016/j.aim.2025.110341.
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