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Given a field F of char(F) = 2, we define un(F) to be the maximal dimension of an anisotropic form in Inq F. For n = 1 it recaptures the definition of u(F). We study the relations between this value and the symbol length of Hn2 (F), denoted by sln2(F). We show for any n ≥ 2 that if 2n ≤ un(F) ≤ u²(F) < ∞, then sln2 (F) ≤ Πni=2(ui(F)/2 + 1 - 2i-1). As a result, if u(F) is finite, then sln2 (F) is finite for any n, a fact which was previously proven when char(F) ≠ 2 by Saltman and Krashen. We also show that if sln2(F) = 1, then un(F) is either 2n or 2n+1. [ABSTRACT FROM AUTHOR]

Let p be an odd prime. Let F be the function field of a p-adic curve. Let A be a central simple algebra of period 2 over F with an involution σ. There are known upper bounds for the u-invariant of hermitian forms over (A, σ). In this article we compute the exact values of the u-invariant of hermitian forms over (A, σ). [ABSTRACT FROM AUTHOR]