Drew Duncan

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20202026

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math.NT2022

Solubility of Additive Forms of Twice Odd Degree over Totally Ramified Extensions of $Q_{2}$

Drew Duncan

We prove that an additive form of degree $d = 2 m$ , $m$ odd over any totally ramified extension of $Q_{2}$ has a nontrivial zero if the number of variables $s$ satisifies $s \g…

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.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…

math.NT2020

Solubility of Additive Forms of Twice Odd Degree 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 $d = 2 m$ , $m$ odd, $m \geq 3$ over the six ramified q…

math.NT2020

Solubility of Additive Sextic Forms over $Q_{2} (- 1)$ and $Q_{2} (- 5)$

Drew Duncan, David B. Leep

Michael Knapp, in a previous work, conjectured that every additive sextic form over $Q_{2} (- 1)$ and $Q_{2} (- 5)$ in seven variables has a nontrivial zero…

Solubility of Additive Forms of Twice Odd Degree over Totally Ramified Extensions of Q2​

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

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

Solubility of Additive Forms of Twice Odd Degree over Ramified Quadratic Extensions of Q2​

Solubility of Additive Sextic Forms over Q2​(−1​) and Q2​(−5​)

Solubility of Additive Forms of Twice Odd Degree over Totally Ramified Extensions of $Q_{2}$

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

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

Solubility of Additive Forms of Twice Odd Degree over Ramified Quadratic Extensions of $Q_{2}$

Solubility of Additive Sextic Forms over $Q_{2} (- 1)$ and $Q_{2} (- 5)$