Diophantine Inequalities for Polynomial Rings

On Diophantine Sets over Polynomial Rings

We prove that the recursively enumerable relations over a polynomial ring R[t], where R is the ring of integers in a totally real number field, are exactly the Diophantine relations over R[t].

On Bernstein Type Inequalities for Complex Polynomial

In this paper, we establish some Bernstein type inequalities for the complex polynomial. Our results constitute generalizations and refinements of some well-known polynomial inequalities.

Differential Polynomial Rings of Triangular Matrix Rings

Symmetric Modular Diophantine Inequalities

In this paper we study and characterize those Diophantine inequalities axmod b ≤ x whose set of solutions is a symmetric numerical semigroup. Given two integers a and b with b = 0 we write a mod b to denote the remainder of the division of a by b. Following the notation used in [8], a modular Diophantine inequality is an expression of the form ax mod b ≤ x. The set S(a, b) of integer solutions ...

The Diophantine Problem for Polynomial Rings and Fields of Rational Functions1

We prove that the diophantine problem for a ring of polynomials over an integral domain of characteristic zero or for a field of rational functions over a formally real field is unsolvable.