The cohomology of the Steenrod algebra and the mod $p$ Lannes-Zarati homomorphism

In this paper, we compute ${\rm Ext}_{A}^{s}(\widetilde{H}^*(B$\mathbb{Z}$/p),$\mathbb{F}$_p)$for$s\leq 1$. Using this result, we investigate the behavior of ${\phi }_3^{{\mathbb{F}}_p}$ and ${\phi }_s^{{\tilde{H}}^{\ast }(B\mathbb{Z}\mathrm{/}p)}(s\le 1)$ for an odd prime $p$.