9 problems

Clunie–Eremenko–Rossi conjecture on zeros of Cauchy transforms with positive coefficients
arXiv@arxiv
Consider the meromorphic Cauchy transform … where $|t_n|\to\infty$ and the series is understood under the usual local convergence condition. Clunie–Eremenko–Rossi conjecture. If…
Conjecturerefutedcauchy-transforms complex-analysis meromorphic-functions
1
Generic non-algebraicity conjecture for smooth Weierstrass cubics
arXiv@arxiv
Smooth Weierstrass cubic period-test conjecture. For a generic smooth real Weierstrass cubic, the compact oval is nonseparating and the exterior Cauchy transform of the domain boun…
Conjectureopenabelian-differentials cauchy-transforms elliptic-curves
0
Non-algebraicity conjecture for smooth one-oval curves of even degree
arXiv@arxiv
Smooth one-oval non-algebraicity conjecture. The exterior Cauchy transform of $\Omega$ is not algebraic.
Conjectureopenalgebraic-curves cauchy-transforms real-algebraic-geometry
1
Multi-oval generic non-algebraicity conjecture for exterior Cauchy transforms
arXiv@arxiv
Multi-oval generic non-algebraicity conjecture. For a generic affine Euclidean realization, the exterior Cauchy transform of the domain bounded by any one of these ovals is non-alg…
Conjectureopenalgebraic-curves cauchy-transforms real-algebraic-geometry
1
Separating/nonseparating algebraicity principle for exterior Cauchy transforms
arXiv@arxiv
Separating/nonseparating algebraicity principle. If $\gamma$ is separating, then the exterior Cauchy transform is algebraic. If $\gamma$ is nonseparating, then the exterior Cauchy…
Conjectureopenabelian-differentials algebraic-curves cauchy-transforms
1
Nuttall's conjecture on Hermite–Padé asymptotics and an unknown Riemann surface
arXiv@arxiv
Hermite–Padé approximants are constructed for a pair of Cauchy transforms, or Markov functions, associated with generally complex measures whose supports overlap. Their asymptotic…
Conjectureopencauchy-transforms hermite-pade-approximation riemann-surfaces
1
Dimension conjecture for quadratic motherbody equations
arXiv@arxiv
Dimension conjecture for quadratic motherbody equations. The set $\Omega_{P,Q}$ is a real semi-analytic variety of real dimension $n$ .
Conjectureopencauchy-transforms measure-theory real-algebraic-geometry
0
Balanced algebraic-function conjecture for positive motherbody measures
arXiv@arxiv
Balanced algebraic-function conjecture. Every such $P(\mathcal C,z)$ admits a positive motherbody measure.
Conjectureopenalgebraic-functions cauchy-transforms measure-theory
0
Uniqueness conjecture for the analytic tree supporting a probability measure
arXiv@arxiv
Uniqueness conjecture. There exists a unique analytic tree $\Gamma$ such that $\mu_\Gamma$ is a probability measure, i.e., $\mu_\Gamma\in\mathfrak{M}^+_{\operatorname{alg}}$ .
Conjectureopencauchy-transforms complex-analysis probability-measures
0