2 citations · 3 across the 8 of their papers we have counts for
10 papers
Rational lines on cubic hypersurfaces II
Julia Brandes, Rainer Dietmann, David B. Leep
We show that any rational cubic hypersurface of dimension at least 33 defined over a number field vanishes on a -rational projective line, reducing the previous lower bound…
Solubility of Additive Forms of Twice Odd Degree over
Drew Duncan, David B. Leep
We prove that an additive form of degree , odd, , over the unramified quadratic extension has a nontrivial zero if the number of variables…
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-…
Solubility of Additive Quartic Forms over Ramified Quadratic Extensions of
Drew Duncan, David B. Leep
We determine the minimal number of variables which guarantees a nontrivial solution for every additive form of degree over the four ramified quadratic extensions…
Solubility of Additive Forms of Twice Odd Degree over Ramified Quadratic Extensions of
Drew Duncan, David B. Leep
We determine the minimal number of variables which guarantees a nontrivial solution for every additive form of degree , odd, over the six ramified q…
Solubility of Additive Sextic Forms over and
Drew Duncan, David B. Leep
Michael Knapp, in a previous work, conjectured that every additive sextic form over and in seven variables has a nontrivial zero…