Yang's critical-line conjecture for the tempered xi function

Determine whether every zero of the tempered xi function \(\widehat\xi(s)\), defined by replacing the hyperbolic cosine in the classical integral representation of the Riemann xi function with a hyperbolic sine, lies on the critical line \(\Re s=1/2\).

Background

Yang introduced the tempered xi function $\widehat\xi(s)$ by replacing the hyperbolic cosine in the classical integral representation of the Riemann xi function with a hyperbolic sine. The conjecture asserts that all zeros of this function lie on the critical line $\Re s=1/2$, equivalently that the associated Fourier sine transform has only real zeros after the standard change of variables.

The paper explicitly presents this as Yang's conjecture and subsequently claims to disprove it by proving that $\widehat\xi$ has infinitely many zeros off the critical line. Thus, although it is stated as a conjecture in the paper, it is not unresolved within the paper's claimed results.