Drew Duncan

activity

20202026

collaborators

6 papers

math.AC2026

A Simple Proof of I. Chowla's Theorem on Addition of Residue Classes

Drew Duncan

We present a brief, elementary proof of a striking theorem by I. Chowla on the addition of residue classes (1937) which generalizes the famous result of Cauchy and Davenport to res…

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…

A Simple Proof of I. Chowla's Theorem on Addition of Residue Classes

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 $Q_{2} (- 5)$