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<p>In 2014, Kumar et al. (Arch Math (Basel) 102:59–70, 2014) proved the existence of uncountably many Liouville tuples whose exponentials are again Liouville and whose generated exponential fields have large transcendence degree. In this note, we extend their result to a geometric setting by requiring the Liouville tuples to satisfy algebraic constraints, namely to lie on prescribed rational affine varieties.</p>

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Liouville points on rational affine varieties

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月25日

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  • Diego Marques

摘要

In 2014, Kumar et al. (Arch Math (Basel) 102:59–70, 2014) proved the existence of uncountably many Liouville tuples whose exponentials are again Liouville and whose generated exponential fields have large transcendence degree. In this note, we extend their result to a geometric setting by requiring the Liouville tuples to satisfy algebraic constraints, namely to lie on prescribed rational affine varieties.