Montgomery's method of polynomial selection for the number field sieve [PDF]
, 2014 The number field sieve is the most efficient known algorithm for factoring large integers that are free of small prime factors. For the polynomial selection stage of the algorithm, Montgomery proposed a method of generating polynomials which relies on ...
Coxon, Nicholas
core +4 more sources
Far-Ultraviolet Number Counts of Field Galaxies [PDF]
, 2011 The far-ultraviolet (FUV) number counts of galaxies constrain the evolution of the star-formation rate density of the universe. We report the FUV number counts computed from FUV imaging of several fields including the Hubble Ultra Deep Field, the Hubble ...
de Mello, Duilia F. +4 more
core +3 more sources
Artificial intelligence in higher education: the state of the field
International Journal of Educational Technology in Higher Education, 2023 This systematic review provides unique findings with an up-to-date examination of artificial intelligence (AI) in higher education (HE) from 2016 to 2022. Using PRISMA principles and protocol, 138 articles were identified for a full examination.
H. Crompton, D. Burke
semanticscholar +1 more source
Nonclassical correlations of photon number and field components in the vacuum state [PDF]
, 2000 It is shown that the quantum jumps in the photon number n from zero to one or more photons induced by backaction evasion quantum nondemolition measurements of a quadrature component x of the vacuum light field state are strongly correlated with the ...
A. Einstein +17 more
core +2 more sources
Special values of adjoint L-functions and congruences for automorphic forms on GL(n) over a number field [PDF]
, 2014 We prove an integrality result for the value at $s=1$ of the adjoint $L$-function associated to a cohomological cuspidal automorphic representation on ${\rm GL}(n)$ over any number field.
B. Balasubramanyam, A. Raghuram
semanticscholar +1 more source
Computing the torsion of the p-ramified module of a number field [PDF]
Mathematics of Computation, 2013 We fix a prime number $p$ and $\K$ a number field, we denote by $M$ the maximal abelian $p$-extension of $\Ko$ unramified outside $p$. The aim of this paper is to study the $\Z_p$-module $\gal(M/\Ko)$ and to give a method to effectively compute its ...
Frédéric Pitoun, Firmin Varescon
semanticscholar +1 more source
Prime Spectrum of the Ring of Adeles of a Number Field
Mathematics, 2022 Much is known about the adele ring of an algebraic number field from the perspective of harmonic analysis and class field theory. However, its ring-theoretical aspects are often ignored.
Álvaro Serrano Holgado
doaj +1 more source
Lattice Sieving in Three Dimensions for Discrete Log in Medium Characteristic
Journal of Mathematical Cryptology, 2020 Lattice sieving in two dimensions has proven to be an indispensable practical aid in integer factorization and discrete log computations involving the number field sieve. The main contribution of this article is to show that a different method of lattice
McGuire Gary, Robinson Oisín
doaj +1 more source
BETTI NUMBERS OF GAUSSIAN FIELDS [PDF]
Journal of The Korean Astronomical Society, 2013 We present the relation between the genus in cosmology and the Betti numbers for excursion sets of three- and two-dimensional smooth Gaussian random fields, and numerically investigate the Betti numbers as a function of threshold level. Betti numbers are topological invariants of figures that can be used to distinguish topological spaces.
Park, Changbom +8 more
openaire +3 more sources
Effects of variations in magnetic Reynolds number on magnetic field distribution in electrically conducting fluid under magnetohydrodynamic natural convection [PDF]
Journal of Heat and Mass Transfer Research, 2017 In this study the effect of magnetic Reynolds number variation on magnetic distribution of natural convection heat transfer in an enclosure is numerically investigated.
Mohsen Pirmohammadi
doaj +1 more source