Title:  On Artin's Conjecture for diagonal forms

Abstract:  Emil Artin conjectured that any form of degree d in more than d^2 variables with coefficients in a p-adic field K has a nontrivial zero in K. Terjanian provided a counterexample to the conjecture, and many more have been found afterwards. However, in the case of diagonal forms, the result is known to hold for K=\mathbb{Q}_p. The conjecture for diagonal forms over arbitrary p-adic fields remains unproved. We investigate partial results.