Add to ORKGconfirmation of Artin’s Conjecture. Let n, t and d1,..., dt be natural numbers. Then Ax and Kochen show that there is a positive integer p0 with the following property. Let K be a p-adic field with [K: Qp] = n, and suppose that f1,..., ft ∈ K[x] are homogeneous with respectiv
AbstractWe prove that a quintic form in 26 variables defined over ap-adic fieldKalways has a nontriv...
AbstractLet k be a global function field with a chosen degree one prime divisor ∞, and O⊂k is the su...
Let K denote a p-adic field and $F_1,..,F_r \in k[x_1, . . . , x_n]$ be forms with respective degree...
This paper is based on Artin's conjecture concerning homogeneous polynomial equations. The conjectur...
AbstractA special case of a conjecture attributed to Artin states that any system of two homogeneous...
We prove a conjecture of Colliot-Thélène that implies the Ax-Kochen Theorem on p-adic forms. We obta...
As a special case of a well-known conjecture of Artin, it is expected that a system of R additive fo...
AbstractWe prove that a quintic form in 26 variables defined over ap-adic fieldKalways has a nontriv...
AbstractLet F be a family of number fields which are normal and of finite degree over a given number...
AbstractLet p be a prime, p ≠ 3or 7. Then any three diagonal cubic forms over the p-adics in at leas...
We prove an analogue of the main result of Buzzard and Taylor [Buzzard, K.; Taylor, R.: Companion fo...
Abstract. We show that Artin’s conjecture concerning p-adic solubility of Diophantine equations fail...
integer a # * 1, or a perfect square, there exist infinitely many primes p for which a is a primiti...
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...
AbstractWe prove that a quintic form in 26 variables defined over ap-adic fieldKalways has a nontriv...
AbstractLet k be a global function field with a chosen degree one prime divisor ∞, and O⊂k is the su...
Let K denote a p-adic field and $F_1,..,F_r \in k[x_1, . . . , x_n]$ be forms with respective degree...
This paper is based on Artin's conjecture concerning homogeneous polynomial equations. The conjectur...
AbstractA special case of a conjecture attributed to Artin states that any system of two homogeneous...
We prove a conjecture of Colliot-Thélène that implies the Ax-Kochen Theorem on p-adic forms. We obta...
As a special case of a well-known conjecture of Artin, it is expected that a system of R additive fo...
AbstractWe prove that a quintic form in 26 variables defined over ap-adic fieldKalways has a nontriv...
AbstractLet F be a family of number fields which are normal and of finite degree over a given number...
AbstractLet p be a prime, p ≠ 3or 7. Then any three diagonal cubic forms over the p-adics in at leas...
We prove an analogue of the main result of Buzzard and Taylor [Buzzard, K.; Taylor, R.: Companion fo...
Abstract. We show that Artin’s conjecture concerning p-adic solubility of Diophantine equations fail...
integer a # * 1, or a perfect square, there exist infinitely many primes p for which a is a primiti...
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...
AbstractWe prove that a quintic form in 26 variables defined over ap-adic fieldKalways has a nontriv...
AbstractLet k be a global function field with a chosen degree one prime divisor ∞, and O⊂k is the su...
Let K denote a p-adic field and $F_1,..,F_r \in k[x_1, . . . , x_n]$ be forms with respective degree...