Zobrazeno 1 - 10
of 98
pro vyhledávání: '"LEEP, DAVID B."'
Autor:
Duncan, Drew, Leep, David B.
We prove that an additive form of degree $d=2m$, $m$ odd, $m\ge3$, over the unramified quadratic extension $\mathbb{Q}_2(\sqrt{5})$ has a nontrivial zero if the number of variables $s$ satisifies $s \ge 4d+1$. If $3 \nmid d$, then there exists a nont
Externí odkaz:
http://arxiv.org/abs/2207.09556
Autor:
Leep, David B., Petrik, Rachel L.
We study lower bound estimates for the number of solutions of systems of equations over finite fields. Heath-Brown improved the lower bounds given by the classical \emph{Chevalley-Warning Theorems} by excluding systems of equations whose solutions fo
Externí odkaz:
http://arxiv.org/abs/2207.04114
Autor:
Duncan, Drew, Leep, David B.
We determine the minimal number of variables $\Gamma^*(d, K)$ which guarantees a nontrivial solution for every additive form of degree $d=4$ over the four ramified quadratic extensions $\mathbb{Q}_2(\sqrt{2}), \mathbb{Q}_2(\sqrt{10}), \mathbb{Q}_2(\s
Externí odkaz:
http://arxiv.org/abs/2112.10854
Autor:
Leep, David B., Petrik, Rachel L.
Publikováno v:
In Finite Fields and Their Applications June 2024 96
Autor:
Duncan, Drew, Leep, David B.
We determine the minimal number of variables $\Gamma^*(d, K)$ which guarantees a nontrivial solution for every additive form of degree $d=2m$, $m$ odd, $m \ge 3$ over the six ramified quadratic extensions of $\mathbb{Q}_2$. We prove that if $K$ is on
Externí odkaz:
http://arxiv.org/abs/2010.06833
Autor:
Duncan, Drew, Leep, David B.
Michael Knapp, in a previous work, conjectured that every additive sextic form over $\mathbb{Q}_2(\sqrt{-1})$ and $\mathbb{Q}_2(\sqrt{-5})$ in seven variables has a nontrivial zero. In this paper, we show that this conjecture is true, establishing th
Externí odkaz:
http://arxiv.org/abs/2005.09770
Autor:
Grimm, David, Leep, David B.
We prove for a large class of fields $F$ that every proper finite extension of $F_{pyth}$, the pythagorean closure of $F$, is not a pythagorean field. This class of fields contains number fields and fields $F$ that are finitely generated of transcend
Externí odkaz:
http://arxiv.org/abs/2001.00618
We study systems of quadratic forms over fields and their isotropy over 2-extensions. We apply this to obtain particular splitting fields for quaternion algebras defined over a finite field extension. As a consequence, we obtain that every central si
Externí odkaz:
http://arxiv.org/abs/1910.01868
Autor:
Leep, David B., Petrik, Rachel L.
Publikováno v:
In Finite Fields and Their Applications August 2023 89
Given a field $F$ of characteristic 2, we prove that if every three quadratic $n$-fold Pfister forms have a common quadratic $(n-1)$-fold Pfister factor then $I_q^{n+1} F=0$. As a result, we obtain that if every three quaternion algebras over $F$ sha
Externí odkaz:
http://arxiv.org/abs/1706.04929