AbstractLet p be a prime, p ≠ 3or 7. Then any three diagonal cubic forms over the p-adics in at least 28 variables possess a common nontrivial p-adic zero. This verifies the Artin conjecture for three diagonal cubic forms over all p-adic fields with the possible exception of Q3 and Q1
AbstractWe show that all p-adic quintic forms in at least n>4562911 variables have a non-trivial zer...
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...
AbstractLet p be a prime, p ≠ 3or 7. Then any three diagonal cubic forms over the p-adics in at leas...
AbstractA special case of a conjecture attributed to Artin states that any system of two homogeneous...
As a special case of a well-known conjecture of Artin, it is expected that a system of R additive fo...
AbstractA special case of a conjecture attributed to Artin states that any system of two homogeneous...
confirmation of Artin’s Conjecture. Let n, t and d1,..., dt be natural numbers. Then Ax and Kochen s...
AbstractLet F be a family of number fields which are normal and of finite degree over a given number...
This paper is based on Artin's conjecture concerning homogeneous polynomial equations. The conjectur...
Abstract. We show that Artin’s conjecture concerning p-adic solubility of Diophantine equations fail...
Let K denote a p-adic field and $F_1,..,F_r \in k[x_1, . . . , x_n]$ be forms with respective degree...
AbstractLet Ms, be the number of solutions of the equation X13 + X23+ … + Xs3=0 in the finite field ...
We discuss the existence of rational and p-adic zeros of systems of cubic forms. In particular, we p...
We give a criterion for the existence of solutions to an equation of the form x3 + ax = b, where a,...
AbstractWe show that all p-adic quintic forms in at least n>4562911 variables have a non-trivial zer...
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...
AbstractLet p be a prime, p ≠ 3or 7. Then any three diagonal cubic forms over the p-adics in at leas...
AbstractA special case of a conjecture attributed to Artin states that any system of two homogeneous...
As a special case of a well-known conjecture of Artin, it is expected that a system of R additive fo...
AbstractA special case of a conjecture attributed to Artin states that any system of two homogeneous...
confirmation of Artin’s Conjecture. Let n, t and d1,..., dt be natural numbers. Then Ax and Kochen s...
AbstractLet F be a family of number fields which are normal and of finite degree over a given number...
This paper is based on Artin's conjecture concerning homogeneous polynomial equations. The conjectur...
Abstract. We show that Artin’s conjecture concerning p-adic solubility of Diophantine equations fail...
Let K denote a p-adic field and $F_1,..,F_r \in k[x_1, . . . , x_n]$ be forms with respective degree...
AbstractLet Ms, be the number of solutions of the equation X13 + X23+ … + Xs3=0 in the finite field ...
We discuss the existence of rational and p-adic zeros of systems of cubic forms. In particular, we p...
We give a criterion for the existence of solutions to an equation of the form x3 + ax = b, where a,...
AbstractWe show that all p-adic quintic forms in at least n>4562911 variables have a non-trivial zer...
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...
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