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Faster polynomial multiplication over finite fields
Let p be a prime, and let M_p(n) denote the bit complexity of multiplying two
polynomials in F_p[X] of degree less than n. For n large compared to p, we
establish the bound M_p(n) = O(n log n 8^(log^* n) log p), where log^* is the
iterated logarithm. This is the first known F\"urer-type complexity bound for
F_p[X], and improves on the previously best known bound M_p(n) = O(n log n log
log n log p)