A variant of Brauer's induction method is developed. It is shown that quartic p-adic forms with at least 9127 variables have non-trivial zeros, for every p. For odd p considerably fewer variables are needed. There are also subsidiary new results concerning quintic forms, and systems of forms. © 2009 London Mathematical Society
Nach einer Vermutung von Artin sollten Systeme aus r Formen vom Grad k mit ganzzahligen Koeffiziente...
The main goal of this note is to describe a new proof of the "exceptional zero conjecture" of Mazur,...
In this thesis, we introduce the notion of quadratic forms and provide motivation for their study. W...
AbstractWe show that all p-adic quintic forms in at least n>4562911 variables have a non-trivial zer...
AbstractWe prove that a quintic form in 26 variables defined over ap-adic fieldKalways has a nontriv...
AbstractUsing the procedure of G. I. Arkhipov and A. A. Karatsuba (Math. USSR-Izv. 19 (1982), 321–34...
In this dissertation, we prove several results about the number of variables necessary to ensure tha...
In this dissertation, we prove several results about the number of variables necessary to ensure tha...
We show that a system of r quadratic forms over a -adic field in at least 4r+1 variables will have a...
In this thesis we discuss the case of p-adic and rational zeros for a pair of additive quartic forms...
We discuss the existence of rational and p-adic zeros of systems of cubic forms. In particular, we p...
AbstractUsing the procedure of G. I. Arkhipov and A. A. Karatsuba (Math. USSR-Izv. 19 (1982), 321–34...
AbstractWe prove that a quintic form in 26 variables defined over ap-adic fieldKalways has a nontriv...
In this paper we consider systems of diagonal forms with integer coefficients in which each form has...
AbstractA special case of a conjecture attributed to Artin states that any system of two homogeneous...
Nach einer Vermutung von Artin sollten Systeme aus r Formen vom Grad k mit ganzzahligen Koeffiziente...
The main goal of this note is to describe a new proof of the "exceptional zero conjecture" of Mazur,...
In this thesis, we introduce the notion of quadratic forms and provide motivation for their study. W...
AbstractWe show that all p-adic quintic forms in at least n>4562911 variables have a non-trivial zer...
AbstractWe prove that a quintic form in 26 variables defined over ap-adic fieldKalways has a nontriv...
AbstractUsing the procedure of G. I. Arkhipov and A. A. Karatsuba (Math. USSR-Izv. 19 (1982), 321–34...
In this dissertation, we prove several results about the number of variables necessary to ensure tha...
In this dissertation, we prove several results about the number of variables necessary to ensure tha...
We show that a system of r quadratic forms over a -adic field in at least 4r+1 variables will have a...
In this thesis we discuss the case of p-adic and rational zeros for a pair of additive quartic forms...
We discuss the existence of rational and p-adic zeros of systems of cubic forms. In particular, we p...
AbstractUsing the procedure of G. I. Arkhipov and A. A. Karatsuba (Math. USSR-Izv. 19 (1982), 321–34...
AbstractWe prove that a quintic form in 26 variables defined over ap-adic fieldKalways has a nontriv...
In this paper we consider systems of diagonal forms with integer coefficients in which each form has...
AbstractA special case of a conjecture attributed to Artin states that any system of two homogeneous...
Nach einer Vermutung von Artin sollten Systeme aus r Formen vom Grad k mit ganzzahligen Koeffiziente...
The main goal of this note is to describe a new proof of the "exceptional zero conjecture" of Mazur,...
In this thesis, we introduce the notion of quadratic forms and provide motivation for their study. W...
DOI
Add to ORKG