Let k be a field and l be a prime, coprime to the characteristic of k. Suppose that k contains the l-th roots of unity. Every element in the Galois cohomology H^{n}(k, μ_{l}) is a sum of “symbols”, thanks to a theorem of Voevodsky. It is interesting to get bounds N(n) such that every such element is a sum of at most N(n) symbols, for fields of arithmetic interest. Using recent results of Saltman, we show that if k is a p-adic field and p not equal to l and K is the function field of a curve over k, then, N(2) = 2 and N(3) = 1.