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arXiv · 2506.07625

Half-Iterates and Delta Conjectures

Steven Finch
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Abstract

The vivid contrast between two competing algorithms for solving Abel's equation $g(\theta(x)) = g(x) + 1$, given $\theta(x)$, is easily sketched. EJ is faster and more efficient, but ML evaluates a limit characterizing the principal solution $g(x)$ directly. EJ finds $g(x)+\delta$, where $\delta$ is possibly nonzero but independent of $x$. If we were to know an exact expression for $\delta$, then the "intrinsicality" of ML would be subsumed by EJ. Filling this gap in our knowledge is the aim of this paper.

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Steven Finch. 2025-06-09. Half-Iterates and Delta Conjectures. https://arxiv.org/abs/2506.07625

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