David B. Leep

collaborators

3 papers

math.NT2022

Solubility of Additive Forms of Twice Odd Degree over $Q_{2} (5)$

Drew Duncan, David B. Leep

We prove that an additive form of degree $d = 2 m$ , $m$ odd, $m \geq 3$ , over the unramified quadratic extension $Q_{2} (5)$ has a nontrivial zero if the number of variables…

math.NT2022

Further Improvements to the Chevalley-Warning Theorems

David B. Leep, Rachel L. Petrik

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-…

math.NT2021

Solubility of Additive Quartic Forms over Ramified Quadratic Extensions of $Q_{2}$

Drew Duncan, David B. Leep

We determine the minimal number of variables $Γ^{*} (d, K)$ which guarantees a nontrivial solution for every additive form of degree $d = 4$ over the four ramified quadratic extensions…

Solubility of Additive Forms of Twice Odd Degree over Q2​(5​)

Further Improvements to the Chevalley-Warning Theorems

Solubility of Additive Quartic Forms over Ramified Quadratic Extensions of Q2​

Solubility of Additive Forms of Twice Odd Degree over $Q_{2} (5)$

Solubility of Additive Quartic Forms over Ramified Quadratic Extensions of $Q_{2}$