$p$-adic Zeros of Quintic Forms

$p$-adic zeros of quintic forms

“…Besides these considerations, we put a general effort on implementing the algorithm efficiently. The full C++ program and the data used in the assembling process are available at [5]. This completes the proof of Theorem 1.…”

On Artin’s conjecture: Linear slices of diagonal hypersurfaces

“…For some other small degrees, the conjecture was confirmed except for a concrete list of small primes. For quintic forms, for example, p-adic solubility is guaranteed for all primes p ≥ 11 (Dumke [14]). Certainly the conjecture was very influential in shaping the subject area, and remains a source of inspiration and inquiry.…”