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Solving low density subset sum problems
  • J. Lagarias, A. Odlyzko
  • Computer Science, Mathematics
  • 24th Annual Symposium on Foundations of Computer…
  • 1983
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
Sets of Matrices All Infinite Products of Which Converge
An infinite product IIT= lMi of matrices converges (on the right) if limi __ M, . . . Mi exists. A set Z = (Ai: i > l} of n X n matrices is called an RCP set (rightconvergent product set) if allExpand
The finiteness conjecture for the generalized spectral radius of a set of matrices
The generalized spectral radius\g9(∑) of a set ∑ of n × n matrices is \g9(∑) = lim supk→∞\g9k(∑)1k, where \g9k(∑) = sup{ϱ(A1A2…Ak): each Ai ∈ ∑}. The joint spectral radius\g9(∑) is \g9(∑) = limExpand
Two-scale difference equations II. local regularity, infinite products of matrices and fractals
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 thatExpand
Two-scale difference equations I: existence and global regularity of solutions
A two-scale difference equation is a functional equation of the form $f(x) = \sum _{n = 0}^N c_n f(\alpha x - \beta _n )$, where $\alpha > 1$ and $\beta _0 < \beta _1 <\cdots <\beta _n $, are realExpand
Tiling with polyominoes and combinatorial group theory
The necessary conditions for the existence of such tilings using boundary invariants are given, which are combinatorial group-theoretic invariants associated to the boundaries of the tile shapes and the regions to be tiled. Expand
Self-affine tiles in ℝn
Abstract A self-affine tile in R n is a set T of positive measure with A ( T )=∪ d ∈ D ( T + d ), where A is an expanding n × n real matrix with |det( A )|= m an integer, and D ={ d ,  d 2 , ...,  dExpand
A bound for the least prime ideal in the Chebotarev Density Theorem
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 expressedExpand
Complements to Li's Criterion for the Riemann Hypothesis☆
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 zetaExpand