This method gives a polynomial time attack on knapsack public key cryptosystems that can be expected to break them if they transmit information at rates below dc (n), as n → ∞.Expand

Abstract In a recent paper Xian-Jin Li showed that the Riemann Hypothesis holds if and only ifλn=∑ρ [1−(1−1/ρ)n] hasλn>0 forn=1, 2, 3, … whereρruns over the complex zeros of the Riemann zeta… Expand

This paper studies solutions of the functional equation \[ f(x) = \sum_{n = 0}^N {c_n f(kx - n),} \] where $k \geqq 2$ is an integer, and $\sum\nolimits_{n = 0}^N {c_n = k} $. Part I showed that… Expand

as x --, oc. In [7] two versions of the Chebotarev density theorem were proved, one unconditional and the other on the assumption of the Generalized Riemann Hypothesis (GRH), each of which expressed… Expand

It is proved that and, where andγj denotes Hermite's constant, are lower bounds for polynomial time computable quantities λ1(L) andΜ(x,L), where Μ( x,L) is the Euclidean distance fromx to the closest vector inL.Expand

It is shown that the problem of deciding whether a given vector α of rational numbers has a simultaneous approximation of specified accuracy with respect to the sup norm with denominator Q in a given interval 1 ≤ Q ≤ N is NP-complete.Expand