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The present remarks concern my paper On Davenport’s bound for the degree of f

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ACTA ARITHMETICA LXXIV.4 (1996)

Acknowledgement of priority

by

Umberto Zannier (Venezia)

The present remarks concern my paper On Davenport’s bound for the degree of f

3

− g

2

and Riemann’s Existence Theorem, published in this jour- nal, 71 (2) (1995), 107–137. I recently discovered the paper Polynomial identities and Hauptmoduln, Quart. J. Math. (2) 32 (1981), 349–370, by W. W. Stothers, which actually covers part of my results, using a method of the same nature. In fact my Proposition 2, p. 120, which proves the ex- istence of cases of equality in Davenport’s bound, is completely contained in Stothers’s results, who actually finds a remarkable exact formula for the number of solutions (Thm. 4.6, p. 362). He also briefly discusses rationality (Thm. 2.4, p. 355), with a method different from mine.

I would also like to avail myself of this opportunity to remark that the genus zero case of the result now well known as the abc-theorem for function fields appears, already in 1981, as Theorem 1.1 of the paper by Stothers.

Ist. Univ. Arch. D.S.T.R.

S. Croce, 191 30135 Venezia, Italy

E-mail: zannier@dimi.uniud.it

Received on 3.11.1995 (2889)

[387]

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