Half-Iterates and Delta Conjectures
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915476414660608 |
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| author | Finch, Steven |
| author_facet | Finch, Steven |
| contents | The vivid contrast between two competing algorithms for solving Abel's equation $g(θ(x)) = g(x) + 1$, given $θ(x)$, is easily sketched. EJ is faster and more efficient, but ML evaluates a limit characterizing the principal solution $g(x)$ directly. EJ finds $g(x)+δ$, where $δ$ is possibly nonzero but independent of $x$. If we were to know an exact expression for $δ$, then the "intrinsicality" of ML would be subsumed by EJ. Filling this gap in our knowledge is the aim of this paper. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_07625 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Half-Iterates and Delta Conjectures Finch, Steven Number Theory Discrete Mathematics 39B12 (Primary) 11B37, 26A18, 39-08, 39B22, 65D20 (Secondary) The vivid contrast between two competing algorithms for solving Abel's equation $g(θ(x)) = g(x) + 1$, given $θ(x)$, is easily sketched. EJ is faster and more efficient, but ML evaluates a limit characterizing the principal solution $g(x)$ directly. EJ finds $g(x)+δ$, where $δ$ is possibly nonzero but independent of $x$. If we were to know an exact expression for $δ$, then the "intrinsicality" of ML would be subsumed by EJ. Filling this gap in our knowledge is the aim of this paper. |
| title | Half-Iterates and Delta Conjectures |
| topic | Number Theory Discrete Mathematics 39B12 (Primary) 11B37, 26A18, 39-08, 39B22, 65D20 (Secondary) |
| url | https://arxiv.org/abs/2506.07625 |