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Tuesday 9/17/02 12:45-1:45 PM in Hylan 1106B:
Mike Knapp- "Artin's conjecture for forms of degree 7 and 11". ABSTRACT: A conjecture commonly attributed to Artin states that a homogeneous polynomial of degree d should have a nontrivial zero in each p-adic field Q_p provided only that the number of variables involved in the polynomial is at least d^2 + 1. While this conjecture is false in general, it turns out to be true if the fields are restricted to Q_p with p sufficiently large. In this talk, I will derive bounds on how large p needs to be in order for the Artin bound to hold. |