$p$-adic Zeros of Quintic Forms
It is shown that a quintic form over a p-adic field with at least 26 variables has a non-trivial zero, providing that the cardinality of the residue class field exceeds 9.
math.NT↗
arXiv subjects
Jan H. Dumke
Publications and source records attributed to Jan H. Dumke.
Quartic Forms in Many Variables
We show that a quartic $p$-adic form with at least $3192$ variables possesses a non-trivial zero. We also prove new results on systems of cubic, quadratic and linear forms. As an example, we show that for a system comprising two cubic forms $132$ variables are sufficient.
math.NT↗