Add to ORKGH. J. S. Smith proved Fermat’s two-square theorem using the notion of palindromic continuants. In this paper we extend Smith’s approach to proper binary quadratic form representations in some commutative Euclidean rings, including rings of integers and rings of polynomials over fields of odd characteristic. Also, we present new deterministic algorithms for finding the corresponding proper representations. © 2015 University of Waterloo. All rights reserved
AbstractA commutative ring A has quadratic stable range 1 (qsr(A) = 1) if each primitive binary quad...
In this paper, representations of positive integers by certain quadratic forms Qp de ned for odd pri...
AbstractIn this paper, we study the representations of a polynomial in the ring F2h[T] as sums A1B1 ...
In 1855 H. J. S. Smith proved Fermat's two-square using the notion of palindromic continuants. In hi...
The association of algebraic objects to forms has had many important applications in number theory. ...
The thesis is concerned with the theory of binary quadratic forms with coefficients in the ring of a...
AbstractWe present algorithms for square classes, quadratic forms and Witt classes of quadratic form...
AbstractIn this paper, we study the number of representations of polynomials of the ringFq[T] by dia...
AbstractIn this article, we provide the complete answer to a question raised by Kitaoka in his book....
In this monograph the authors extend the classical algebraic theory of quadratic forms over fields t...
It is our basic question to study the following Diophantine equations (1.1) tXAX = B over the ring o...
Abstract. This paper presents fundamental algorithms for computational theory of quadratic forms ove...
Abstract. We present a theory of classifying quadratic forms over an algebraic number field which is...
The book deals with algorithmic problems related to binary quadratic forms, such as finding the repr...
It is shown that the set of prime integers in Q( 2) is partitioned into two sets with respect to the...
AbstractA commutative ring A has quadratic stable range 1 (qsr(A) = 1) if each primitive binary quad...
In this paper, representations of positive integers by certain quadratic forms Qp de ned for odd pri...
AbstractIn this paper, we study the representations of a polynomial in the ring F2h[T] as sums A1B1 ...
In 1855 H. J. S. Smith proved Fermat's two-square using the notion of palindromic continuants. In hi...
The association of algebraic objects to forms has had many important applications in number theory. ...
The thesis is concerned with the theory of binary quadratic forms with coefficients in the ring of a...
AbstractWe present algorithms for square classes, quadratic forms and Witt classes of quadratic form...
AbstractIn this paper, we study the number of representations of polynomials of the ringFq[T] by dia...
AbstractIn this article, we provide the complete answer to a question raised by Kitaoka in his book....
In this monograph the authors extend the classical algebraic theory of quadratic forms over fields t...
It is our basic question to study the following Diophantine equations (1.1) tXAX = B over the ring o...
Abstract. This paper presents fundamental algorithms for computational theory of quadratic forms ove...
Abstract. We present a theory of classifying quadratic forms over an algebraic number field which is...
The book deals with algorithmic problems related to binary quadratic forms, such as finding the repr...
It is shown that the set of prime integers in Q( 2) is partitioned into two sets with respect to the...
AbstractA commutative ring A has quadratic stable range 1 (qsr(A) = 1) if each primitive binary quad...
In this paper, representations of positive integers by certain quadratic forms Qp de ned for odd pri...
AbstractIn this paper, we study the representations of a polynomial in the ring F2h[T] as sums A1B1 ...