A diophantine equation over a function field

J. W. S. Cassels

Type: Article

Publication Date: 1978-06-01

Citations: 6

DOI: https://doi.org/10.1017/s1446788700021479

Abstract

Abstract Let x 0 , x 1 , x 2 , x 3 be polynomials in a variable t and with coefficients in a field k of character of characteristic 0. If and , then x 0 = x 1 = x 2 = x 3 = 0. This partially answers a question of Pjatetskii-Š;apiro and Šafarevič about the K 3-surface . The proof uses a technique of M. R. Christie.

Locations

Journal of the Australian Mathematical Society - View - PDF

Similar Works

Action	Title	Year	Authors
+	A Polynomial Diophantine Equation (M. S. Klamkin)	1974	O.P. Lossers
+ PDF Chat	A diophantine equation	1985	J. W. S. Cassels
+ PDF Chat	An indeterminate equation	1981	V. A. Dem’yanenko
+ PDF Chat	On the diophantine equation f(x)f(y)=f(z)2	2007	Maciej Ulas
+ PDF Chat	On the Diophantine Equation $(x^2+k)(y^2+k)=(z^2+k)^2$	2008	Maciej Ulas
+ PDF Chat	DIOPHANTINE EQUATIONS OF THE FORM OVER FUNCTION FIELDS	2023	Anwesh Ray
+	A Diophantine Equation	1985	P. D. T. A. Elliott
+	A note on the Diophantine equation $$f(x)f(y)=f(z^2)$$ f ( x ) f ( y ) = f ( z 2 )	2015	Yong Zhang Tianxin Cai
+	A Polynomial Diophantine Equation	1973	M. S. Klamkin
+	Diophantine Equations in Many Variables	2014	Jan H. Dumke
+	Diophantine Equations in Many Variables	2014	Jan H. Dumke
+	A quadratic diophantine equation	1963	Amin Muwafi
+	The Diophantine Equation f(x) = g(y)	1990	Todd Cochrane
+	On the diophantine equation f (x, y) = 0.	1976	Howard Kleiman
+ PDF Chat	On the Diophantine equation $1^k+2^k+\dotsb+x^k=y^n$	2004	Michael A. Bennett Kálmán Győry Ákos Pintér
+ PDF Chat	On a Diophantine equation	1979	Saburô Uchiyama
+	On a Diophantine Equation	2021	Nguyen Xuan Tho
+ PDF Chat	On a diophantine equation	1960	J. W. S. Cassels
+	On a diophantine equation	2016	В. К. Леонтьев
+	On a Diophantine equation	2017	Xin Zhang

Works That Cite This (6)

Action	Title	Year	Authors
+	John William Scott (‘Ian’) Cassels. 11 July 1922 — 27 July 2015	2023	Rainer Dietmann Tom Fisher Chris Smyth Sanju Velani
+ PDF Chat	Fields of definition of singular K3 surfaces	2007	Matthias Schütt
+	Lines on Fermat surfaces	2010	Matthias Schütt Tetsuji Shioda Ronald van Luijk
+	Modular forms and K3 surfaces	2013	Noam D. Elkies Matthias Schütt
+ PDF Chat	Two Lectures on the Arithmetic of K3 Surfaces	2013	Matthias Schütt
+	Diophantine equations over ℂ(t) and complex multiplication	1979	Harvey Cohn

Works Cited by This (2)

Action	Title	Year	Authors
+ PDF Chat	An indeterminate equation	1981	V. A. Dem’yanenko
+	Positive definite rational functions of two variables which are not the sum of three squares	1976	M.R Christie