Extension of the Equal Ripple Theorem to the first Zolotarev problem on two complex intervals

Let $S_e$ and $S_p$ be the two intervals in $C$, and let $t_e(s)/t_e(-s)$ and $t_p(s)/t_p(-s)$ be solutions of the Zolotarev problems on $S_e$ and $S_p$, respectively. The arrays $bbda_1$, $bbda_2$, and $bbda_3$ determine the intervals, while $l$ is the degree of $t_e$ and the degree of $t_p$ is $k-l$.

Extended Equal Ripple conjecture. There are infinitely many arrays $bbda_1,bbda_2,bbda_3$ for which there exists $l$ such that

$$\max_{S_e}\left|\frac{t_e(s)}{t_e(-s)}\right|=\max_{S_p}\left|\frac{t_p(s)}{t_p(-s)}\right|.$$

If the stated condition

is valid, then $t=t_et_p$ solves the global Zolotarev problem

.

This proposes an extension of the Equal Ripple Theorem from real rational approximation on one interval to the first Zolotarev problem on two complex intervals. The source does not provide evidence that the conjecture has been resolved.