2 problems

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The conjecture for sums of powers of quadratic polynomials
Conjecture for sums of powers of quadratic polynomials. If $f\in\mathcal{QP}_n$ , then $f$ has at most $2n-1$ real critical points. Moreover, if $\alpha$ is a negative integer, each…
Conjectureopencritical-points polynomial-zeros real-rational-functionsarXiv posted 2 days ago
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Conjecture on solutions of interlacing real rational equations
Conjecture on the solutions. All solutions of this equation, except possibly one and counting multiplicity, lie in the disk $|z|<\lambda_n$ .
Conjectureopencomplex-analysis interlacing-polynomials real-rational-functionsarXiv posted 2 days ago

The conjecture for sums of powers of quadratic polynomials