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Let be a prime, and let denote the bit complexity of multiplying two polynomials in of degree less than . For large compared to , we establish the bound , where is the iterated logarithm. This is the first known Fürer-type complexity bound for , and improves on the previously best known bound .

**Authors:**

**Keywords: **Polynomial multiplication, finite field,
algorithm, complexity bound, FFT

**A.M.S. subject classification: **68W30, 68Q17, 68W40