DIOPHANTINE EQUATIONS OF THE FORM OVER FUNCTION FIELDS

Diophantine Equations and Congruences over Function Fields

We generalize the methods of Pierce of counting solutions to the congruence X ≡ Y b mod D [8] and the square sieve method of counting squares in the sequence f(X) + g(Y ) [7] to the function field setting.

Diophantine Equations over Global Function Fields II: R-Integral Solutions of Thue Equations

Solving resultant form equations over number fields

We give an efficient algorithm for solving resultant form equations over number fields. This is the first time that such equations are completely solved by reducing them to unit equations in two variables.

Diophantine Equations in Cyclotomic Fields

where p is a given rational prime? It is almost trivial (from the theory of the Gaussian sum or otherwise) that a solution exists with g =p; it is less trivial that a solution also exists when g = p+p+l; but it is not asserted that solutions do not exist for other values of g. While we are unable to give anything like a complete answer to the problem proposed, we can prove something in this dir...

Diophantine Inequalities in Function Fields

This paper develops the Bentkus-Götze-Freeman variant of the DavenportHeilbronn method for function fields in order to count Fq[t]-solutions to diagonal Diophantine inequalities in Fq((1/t)).