AbstractWe prove that every cubic form in 16 variables over an algebraic number field represents zero, generalizing the corresponding result of Davenport for cubic forms over the rationals. (This has already been proved for cubic forms in 17 or more variables by Ryavec.) We present this result as a special case of a “local-implies-global” theorem for cubic polynomials
Let K denote a p-adic field and $F_1,..,F_r \in k[x_1, . . . , x_n]$ be forms with respective degree...
We use recent results about linking the number of zeros on algebraic varieties over $\mathbb{C}$, de...
In this thesis, we introduce the notion of quadratic forms and provide motivation for their study. W...
AbstractWe prove that every cubic form in 16 variables over an algebraic number field represents zer...
The goal of this thesis is to study possible generalizations of a theorem of Nakagawa, first stated ...
AbstractWe extend to finite fields in general the results proved, in a recent paper (J. Number Theor...
A reduction theory is developed for binary forms (homogeneous polynomials) of degrees three and four...
In this dissertation we investigate the existence of a nontrivial solution to a system of two quadra...
AbstractLet K be an algebraic number field of finite degree over the rationals. The two themes of th...
In this thesis we study several problems related to the representation of integers by binary forms a...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135196/1/blms0556.pd
AbstractWe prove that a quintic form in 26 variables defined over ap-adic fieldKalways has a nontriv...
We show that if a universal quadratic form exists over an infinite degree, totally real extension of...
Let be a quadratic form in variables defined on a vector space over a global field , and be a fi...
We discuss the existence of rational and p-adic zeros of systems of cubic forms. In particular, we p...
Let K denote a p-adic field and $F_1,..,F_r \in k[x_1, . . . , x_n]$ be forms with respective degree...
We use recent results about linking the number of zeros on algebraic varieties over $\mathbb{C}$, de...
In this thesis, we introduce the notion of quadratic forms and provide motivation for their study. W...
AbstractWe prove that every cubic form in 16 variables over an algebraic number field represents zer...
The goal of this thesis is to study possible generalizations of a theorem of Nakagawa, first stated ...
AbstractWe extend to finite fields in general the results proved, in a recent paper (J. Number Theor...
A reduction theory is developed for binary forms (homogeneous polynomials) of degrees three and four...
In this dissertation we investigate the existence of a nontrivial solution to a system of two quadra...
AbstractLet K be an algebraic number field of finite degree over the rationals. The two themes of th...
In this thesis we study several problems related to the representation of integers by binary forms a...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135196/1/blms0556.pd
AbstractWe prove that a quintic form in 26 variables defined over ap-adic fieldKalways has a nontriv...
We show that if a universal quadratic form exists over an infinite degree, totally real extension of...
Let be a quadratic form in variables defined on a vector space over a global field , and be a fi...
We discuss the existence of rational and p-adic zeros of systems of cubic forms. In particular, we p...
Let K denote a p-adic field and $F_1,..,F_r \in k[x_1, . . . , x_n]$ be forms with respective degree...
We use recent results about linking the number of zeros on algebraic varieties over $\mathbb{C}$, de...
In this thesis, we introduce the notion of quadratic forms and provide motivation for their study. W...