算术概率测度
Arithmetic probability measures
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中文总结 AI 辅助
本文研究复平面紧子集上由代数整数伽罗瓦共轭极限分布产生的算术概率测度，证明该类测度只需验证两个条件即可满足无穷多积分不等式，特定紧集下等价于检查两个整数多项式对应的不等式。
中文摘要 AI 辅助
我们研究由某些代数整数的伽罗瓦共轭的极限分布所产生的复平面紧子集上的概率测度。这类测度具有无穷多个积分不等式的特征，每个非零整数多项式对应一个不等式。我们研究由调和测度与平衡测度的特定凸组合构成的一大类测度，随后证明对于该类中的测度，只需验证两个条件即可保证所有所需不等式成立。在基础紧集满足额外算术约束的情况下，我们进一步证明这无穷多组不等式等价于检查两个明确指定的整数多项式对应的不等式。
英文摘要
We consider probability measures on compact subsets of the complex plane arising as limiting distributions of Galois conjugates of certain algebraic integers. These measures are characterized by infinitely many integral inequalities, one for each nonzero integer polynomial. We study a broad family of measures given by particular convex combinations of harmonic and equilibrium measures. We then show that, for measures in this family, it suffices to verify two conditions to guarantee all the required inequalities. Under additional arithmetic constraints on the underlying compact sets, we further show that the infinite collection of inequalities is equivalent to checking the inequalities associated with two explicitly specified integer polynomials.
发表机构
- Faculty of Engineering and Natural Sciences, Sabancı University（萨班奇大学工程与自然科学学院）
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