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<p>We study the generating series associated with the degree sequence of a monomial self-map of a projective toric variety. We establish conditions under which this series has its circle of convergence as a natural boundary, and hence is a transcendental, non-holonomic function. In the case of toric surfaces, our results are sharp; moreover, we answer a question of Bell by proving that its reduction modulo <i>p</i> is transcendental for all but finitely many prime numbers <i>p</i>.</p>

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On the generating series of the degree sequence

  • 期刊论文

  • 发表日期：

    2026年8月1日

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  • Quang-Khai Nguyen

摘要

We study the generating series associated with the degree sequence of a monomial self-map of a projective toric variety. We establish conditions under which this series has its circle of convergence as a natural boundary, and hence is a transcendental, non-holonomic function. In the case of toric surfaces, our results are sharp; moreover, we answer a question of Bell by proving that its reduction modulo p is transcendental for all but finitely many prime numbers p.