A diophantine equation over a function field

Author:

Cassels J. W. S.

Abstract

AbstractLet x0, x1, x2, x3 be polynomials in a variable t and with coefficients in a field k of character of characteristic 0. If and , then x0 = x1 = x2 = x3 = 0. This partially answers a question of Pjatetskii-Š;apiro and Šafarevič about the K3-surface . The proof uses a technique of M. R. Christie.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference4 articles.

1. Torelli's theorem for K3 algebraic surfaces;Pjatetskii-Sapiro;Izv. Akad. Nauk SSSR (ser. mat.),1971

2. Positive definite rational functions of two variables which are not the sum of three squares

3. indeterminate equation;Dem'janenko;Zap. Naucn, Sem. Leningrad. Otdel. Mat. Inst. Steklov,1977

4. Étude des points d'ordre fini des variétés abeliennes de dimension un définies sur un anneau principal;Hellegouarch;J. reine. angew. Math.,1970

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. John William Scott (‘Ian’) Cassels. 11 July 1922 — 27 July 2015;Biographical Memoirs of Fellows of the Royal Society;2023-03-29

2. Modular forms and K3 surfaces;Advances in Mathematics;2013-06

3. Two Lectures on the Arithmetic of K3 Surfaces;Fields Institute Communications;2013

4. Lines on Fermat surfaces;Journal of Number Theory;2010-09

5. Diophantine equations over ℂ(t) and complex multiplication;Number Theory Carbondale 1979;1979

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