22 research outputs found
Close to Uniform Prime Number Generation With Fewer Random Bits
In this paper, we analyze several variants of a simple method for generating
prime numbers with fewer random bits. To generate a prime less than ,
the basic idea is to fix a constant , pick a
uniformly random coprime to , and choose of the form ,
where only is updated if the primality test fails. We prove that variants
of this approach provide prime generation algorithms requiring few random bits
and whose output distribution is close to uniform, under less and less
expensive assumptions: first a relatively strong conjecture by H.L. Montgomery,
made precise by Friedlander and Granville; then the Extended Riemann
Hypothesis; and finally fully unconditionally using the
Barban-Davenport-Halberstam theorem. We argue that this approach has a number
of desirable properties compared to previous algorithms.Comment: Full version of ICALP 2014 paper. Alternate version of IACR ePrint
Report 2011/48
Some Additive Combinatorics Problems in Matrix Rings
We study the distribution of singular and unimodular matrices in sumsets in
matrix rings over finite fields. We apply these results to estimate the largest
prime divisor of the determinants in sumsets in matrix rings over the integers
Proof of a conjecture of Polya on the zeros of successive derivatives of real entire functions
We prove Polya's conjecture of 1943: For a real entire function of order
greater than 2, with finitely many non-real zeros, the number of non-real zeros
of the n-th derivative tends to infinity with n. We use the saddle point method
and potential theory, combined with the theory of analytic functions with
positive imaginary part in the upper half-plane.Comment: 26 page
Unambiguous discrimination between two unknown qudit states
We consider the unambiguous discrimination between two unknown qudit states
in -dimensional () Hilbert space. By equivalence of unknown
pure states to known mixed states and with the Jordan-basis method, we
demonstrate that the optimal success probability of the discrimination between
two unknown states is independent of the dimension . We also give a scheme
for a physical implementation of the programmable state discriminator that
unambiguously discriminate between two unknown states with optimal probability
of success.Comment: 8 pages, 3 figure
Nonmonotonic inelastic tunneling spectra due to surface spin excitations in ferromagnetic junctions
The paper addresses inelastic spin-flip tunneling accompanied by surface spin
excitations (magnons) in ferromagnetic junctions. The inelastic tunneling
current is proportional to the magnon density of states which is
energy-independent for the surface waves and, for this reason, cannot account
for the bias-voltage dependence of the observed inelastic tunneling spectra.
This paper shows that the bias-voltage dependence of the tunneling spectra can
arise from the tunneling matrix elements of the electron-magnon interaction.
These matrix elements are derived from the Coulomb exchange interaction using
the itinerant-electron model of magnon-assisted tunneling. The results for the
inelastic tunneling spectra, based on the nonequilibrium Green's function
calculations, are presented for both parallel and antiparallel magnetizations
in the ferromagnetic leads.Comment: 9 pages, 4 figures, version as publishe
Representations of the Weyl Algebra in Quantum Geometry
The Weyl algebra A of continuous functions and exponentiated fluxes,
introduced by Ashtekar, Lewandowski and others, in quantum geometry is studied.
It is shown that, in the piecewise analytic category, every regular
representation of A having a cyclic and diffeomorphism invariant vector, is
already unitarily equivalent to the fundamental representation. Additional
assumptions concern the dimension of the underlying analytic manifold (at least
three), the finite wide triangulizability of surfaces in it to be used for the
fluxes and the naturality of the action of diffeomorphisms -- but neither any
domain properties of the represented Weyl operators nor the requirement that
the diffeomorphisms act by pull-backs. For this, the general behaviour of
C*-algebras generated by continuous functions and pull-backs of homeomorphisms,
as well as the properties of stratified analytic diffeomorphisms are studied.
Additionally, the paper includes also a short and direct proof of the
irreducibility of A.Comment: 71 pages, 1 figure, LaTeX. Changes v2 to v3: previous results
unchanged; some addings: inclusion of gauge transforms, several comments,
Subsects. 1.5, 3.7, 3.8; comparison with LOST paper moved to Introduction;
Def. 2.5 modified; some typos corrected; Refs. updated. Article now as
accepted by Commun. Math. Phy