The proofs of the results of the sections 4 and 5 depend heavily on the deep works of Carlitz and Uchiyama, Deligne, Lang and Weil, and Bombieri, because the essential difficulty was that of estimating an exponential sum. It looks possible that in some cases this difficulty could be avoided by relating the demands of (8) and (9) to the estimate given by (10). This approach might lead to elementary proofs and at least it improves some bounds for acceptable n's. In fact, the bounds like (13) are not very precise, being merely given for convenience, and they could be improved at the cost of considerable complications. Of course it would be nice to find precise bounds.