2 problems

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Conjecture on complex branches for irrational parameters of a generalised Lambert function
Complex-branch analysis conjecture. The analysis of complex branches for irrational $a$ should mirror the analysis for rational $a$ , barring periodicity.
Conjectureopencomplex-analysis inverse-functions lambert-functionsarXiv posted 2 days ago
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Conjecture on real branch singularities of the principal inverse zeta branch
Let $s_1=zeta^{-1}(w)$ be the principal branch of the inverse Riemann zeta function, and let $j_1$ denote the lowest zero described in the surrounding discussion. The strip…
Conjectureopencomplex-analysis inverse-functions riemann-zeta-functionarXiv posted 2 days ago

Conjecture on complex branches for irrational parameters of a generalised Lambert function