A Reply
                           Zhou Xueguang



                         September 22, 2003

    As I think that your argument on D. Ravenel's proof of non-existence of

V(3) at p=5 is incorrect (top of P.5 on your paper). Sure we could not get

the conclusion that dr(fl3) 6= 0 from fi1716= 0.  But D. Ravenel's idea is as

following.

    Firstly, he proved that fi211= 0, (indeed it is a result from Toda) and

d33(ff1fi45=5) = fi211. Then he says that ff1fi45=5is a linear combination of f*
 *i31fl3,

3_fi31fi14 and fi1x761, i.e.  ff1fi45=5= k1fi31fl3 + k23_fi31fi14+ k3fi1x761.  *
 *But 3_fi31fi14

and fi1x761are permanent cycles. So


           d33(k1fi31fl3 + k23_fi31fi14+ k3fi1x761) = d33(k1fi31fl3) = fi211


And then k1 6= 0 and


                     d33(k1fi31fl3) = k1fi31d33(fl3) = fi211


    Sure I did not check his computation. Maybe Nakai who is at Rochester

now did. As K. Shimomura says, he did not check D. Ravenel's computation

neither, but D. Ravenel is computing ßn(S0) at p = 5 whthin n   6000 lately.

So he might recomputed that.



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