Half-Iterates and Delta Conjectures

Steven Finch

Half-Iterates and Delta Conjectures

Number Theory 2025-09-04 v6 Discrete Mathematics

Authors: Steven Finch

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.

Keywords

random matrix ensembles

Cite

@article{arxiv.2506.07625,
  title  = {Half-Iterates and Delta Conjectures},
  author = {Steven Finch},
  journal= {arXiv preprint arXiv:2506.07625},
  year   = {2025}
}

Comments

Two distinct earlier preprints are relevant. The first covers half-iterates of $x(1+x)$, sin$(x)$ & exp$(x/e)$ and appears at arXiv:2506.07625v1. The second covers half-iterates of $x$exp$(x)$, $x+1/x$ & arcsinh$(x)$ and appears at arXiv:2506.07625v2. Reading these will help to motivate the study of $\delta$ in the current paper. 9 pages; 2 figures

Half-Iterates and Delta Conjectures

Abstract

Keywords

Cite

Comments

Related papers