关于次数序列的生成级数
On the generating series of the degree sequence
AI总结：
该研究探究射影环面簇单项式自映射次数序列的生成级数，明确其为超越非全纯函数的条件，针对环面曲面给出最优结果并解答Bell关于模素数约化超越性的问题。
摘要：
我们研究与射影环面簇的单项式自映射的次数序列相关的生成级数，确定该级数以收敛圆为自然边界的条件，证明其为超越的非全纯函数。对于环面曲面，我们的结果是最优的，此外通过证明其模素数p的约化结果对除有限个素数p外均为超越函数，回答了Bell提出的问题。
英文摘要：
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 $p$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
