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

For any pointed space X, the mod p Lannes-Zarati homomorphism φsH˜⁎X is considered as a graded associated version of the mod p Hurewicz map h⁎:π⁎(QX) → H⁎QX in the E2 -term of the Adams spectral sequence. In this paper, we investigate the behavior of φ3Fp and φsH˜⁎(BZ/p) (s ≤ 1) for an odd prime p.