Beyond Artin's Conjecture for Cubic Forms

Two Cases of Artin's Conjecture

“…This chapter comprises the authors article Beyond Artin's Conjecture for Cubic Forms [24]. It contains the proof of the following theorem, which claims that for one diagonal cubic form f and one linear form g in s variables the equations f = g = 0 have a non-trivial p-adic solution for all primes p provided that s ≥ 8.…”