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

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

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

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

Fast Reduction and Composition of Binary Quadratic Forms is studied in detail in the context of binary quadratic forms and its application to discrete geometry.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