By combining Pan’s trilinear technique with a strong version of the compression theorem for the case of several disjoint matrix multiplications it is shown that multiplication of N \times N matrices (over arbitrary fields) is possible in time.Expand

Under reasonable assumptions, polynomial multiplication and discrete Fourier transforms of length n and in l-bit precision are possible in time O(ψ (nl), and division of polynomials in O(n(l+n))).Expand

Extended quasi-gcd computation means to find such h and additional cofactors u, ν such that uf + νg − h − h is an ϵ-approximate divisor of f and of g.Expand

This paper gives a complete description of the SMM model and its real time equivalence to the so-called successor RAMS and shows the existence of an SMM that performs integer-multiplication in linear time.Expand

The best previously know algorithm for evaluating the Riemann zeta function, ζ(σ+it), with σ bounded and t large to moderate accuracy was based on the Rienmann-Siegel formula and required on the… Expand

All steps described in the preceding section for fixed m are certainly covered by the rather crude bound of \(O(m(n(n^{5 + \varepsilon } + n^3 (log|f|)^{2 + Â£3) (log | f|)}{2} ))\) bit operations, so the final time bound is obtained.Expand

Abstract The length l of addition chains for z is shown to be bounded from below by log 2 z + log 2 s ( z )−2.13, where s ( z ) denotes the sum of the digits in the binary expansion of z . The proof… Expand

We study the power of deterministic successor RAM's with extra instructions like +,*,⋎ and the associated classes of problems decidable in polynomial time. Our main results are NP ... PTIME (+,*,⋎)… Expand