Miriam Kaesberg, Göttingen University

April 23rd, 2021 4:00-5:00 pm CET

Title : On Artin’s Conjecture: Pairs of Additive Forms

Abstract :

A conjecture by Emil Artin claims that for forms f₁, ..., f_r ∊ Z[x₁, ..., x_s] of degree k₁, ..., k_r the system of equation f₁ = f₂ = ... = f_r = 0 has a non-trivial p-adic solution for all primes p provided that s > k₁²+ ... + k_r². Although this conjecture was disproved in general, it holds in some cases. In this talk I will focus on the case of two additive forms with the same degree k and sketch the proof that Artin’s conjecture holds in this case unless k = 2^t for 2 ≤ t ≤ 15 and k = 3 * 2^t for 2 ≤ t.