On eigenfunctions of the kernel $\frac{1}{2}+\lfloor \frac{1}{xy}\rfloor -\frac{1}{xy}$

Nigel Watt

The integral kernel $K(x,y):=\frac{1}{2}+\lfloor \frac{1}{xy}\rfloor -\frac{1}{xy}$ ($0<x,y\le 1$) has connections with the Riemann zeta-function and a (recently observed) c…