We define and analyze quantum computational variants of random walks on one-dimensional lattices, including the Hadamard walk, a quantum analog of the symmetric random walk.Expand

We show that clause-final verbal clusters in Standard Dutch and German differ strikingly in the kinds of dependencies they normally permit between verbs and their arguments, with Dutch preferring crossed dependencies and German nested.Expand

Many number-theoretic algorithms rely on a result of Ankeny, which states that if the Extended Riemann Hypothesis (ERH) is true, any nontrivial multiplicative subgroup of the integers modulo m omits… Expand

We prove the following theorems, assuming the Extended Riemann Hypothesis: There is a degree-1 prime p of K such that (p/E/K) generates the same group as σ, satisfying Np ≤ (1 + o(1))(log Δ) 2 .Expand

This note discusses the relationship between the two problems of the title. We present probabilistic polynomial-time reduction that show: 1) To factor n, it suffices to be able to compute discrete… Expand

This book makes a substantial contribution to the understanding of a murky area of number theory that is important to computer science, an area relevant to the design and analysis of number-theoretic… Expand