Fast multiplication of integer matrices Withdrawn paper

Erratum. Eric Schost discovered a bug in this paper: by construction, formula (7) does not hold, since the matrix Va,n is not invertible whenever l> 2. Unfortunately, we do not see how to repair this bug: not only Va,n is not invertible, but the rank of Va,n is actually very small (and equal to max {q1, , ql}). This makes the proof collapse. We have also tried a few other things, such as fixing a=2 and trying to take many qi for which a is a primitive root of unity of a small order. This also does not work, since the product of two operators in Z[X, Q]2 makes the coefficient sizes increase by n2 (and not merely n) bits. Going until “small order n”, we must have q1 ql P lcm(21 − 1, 22 − 1, , 2− 1). This lcm is of the same order as 2 2 , but strictly smaller than 2 2 .