15,157 research outputs found

    Faster truncated integer multiplication

    Full text link
    We present new algorithms for computing the low n bits or the high n bits of the product of two n-bit integers. We show that these problems may be solved in asymptotically 75% of the time required to compute the full 2n-bit product, assuming that the underlying integer multiplication algorithm relies on computing cyclic convolutions of real sequences.Comment: 28 page

    Computing zeta functions of arithmetic schemes

    Full text link
    We present new algorithms for computing zeta functions of algebraic varieties over finite fields. In particular, let X be an arithmetic scheme (scheme of finite type over Z), and for a prime p let zeta_{X_p}(s) be the local factor of its zeta function. We present an algorithm that computes zeta_{X_p}(s) for a single prime p in time p^(1/2+o(1)), and another algorithm that computes zeta_{X_p}(s) for all primes p < N in time N (log N)^(3+o(1)). These generalise previous results of the author from hyperelliptic curves to completely arbitrary varieties.Comment: 23 pages, to appear in the Proceedings of the London Mathematical Societ

    Smart meters might be the only way to escape the Big Six and their overpriced energy

    Get PDF
    The UK is a rich, stable country with oil and gas reserves, lots of wind, and more than enough scientists and engineers to make the most of its resources. So why do so many people in the country continue to tolerate high energy bills and poor service
    • …
    corecore