Abstract

This paper studies Iwasawa invariants in anti-cyclotomic towers. We do this by proposing two heuristics supported by computations. First we propose the Intersection Heuristics: these model “how often” the p-Hilbert class field of an imaginary quadratic field intersects the anti-cyclotomic tower and to what extent. Second we propose the Invariants Heuristics: these predict that the Iwasawa invariants λ$\lambda$$\lambda$ and μ$\mu$$\mu$ usually vanish for imaginary quadratic fields where p is non-split.

中文翻译：

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反分圆 ℤp-扩展的启发式方法

摘要

本文研究了反分圆塔中的 Iwasawa 不变量。我们通过提出两种由计算支持的启发式方法来做到这一点。首先，我们提出相交启发法：这些模型模拟了虚二次场的p-希尔伯特类场与反分圆塔相交的“频率”以及相交的程度。其次，我们提出不变量启发式：这些预测 Iwasawa 不变量λ$\lambda$$\lambda$和μ$\mu$$\mu$对于p不可分裂的虚二次场，通常消失。