Results 31 to 40 of about 1,187,567 (336)

Short Principal Ideal Problem in multicubic fields

Journal of Mathematical Cryptology, 2020
One family of candidates to build a post-quantum cryptosystem upon relies on euclidean lattices. In order to make such cryptosystems more efficient, one can consider special lattices with an additional algebraic structure such as ideal lattices.
Lesavourey Andrea, Plantard Thomas, Susilo Willy   +2 more
doaj   +1 more source

Bicyclic commutator quotients with one non-elementary component [PDF]

Mathematica Bohemica, 2023
For any number field $K$ with non-elementary $3$-class group ${\rm Cl}_3(K)\simeq C_{3^e}\times C_3$, $e\ge2$, the punctured capitulation type $\varkappa(K)$ of $K$ in its unramified cyclic cubic extensions $L_i$, $1\le i\le4$, is an orbit under the ...
Daniel C. Mayer
doaj   +1 more source

Elementary Fractal Geometry. 2. Carpets Involving Irrational Rotations

Fractal and Fractional, 2022
Self-similar sets with the open set condition, the linear objects of fractal geometry, have been considered mainly for crystallographic data. Here we introduce new symmetry classes in the plane, based on rotation by irrational angles.
Christoph Bandt, Dmitry Mekhontsev
doaj   +1 more source

The Ring-LWE Problem in Lattice-Based Cryptography: The Case of Twisted Embeddings

Entropy, 2021
Several works have characterized weak instances of the Ring-LWE problem by exploring vulnerabilities arising from the use of algebraic structures. Although these weak instances are not addressed by worst-case hardness theorems, enabling other ring ...
Jheyne N. Ortiz, Robson R. de Araujo, Diego F. Aranha, Sueli I. R. Costa, Ricardo Dahab   +4 more
doaj   +1 more source

Gr\"obner Bases over Algebraic Number Fields

, 2015
Although Buchberger's algorithm, in theory, allows us to compute Gr\"obner bases over any field, in practice, however, the computational efficiency depends on the arithmetic of the ground field.
Boku, Dereje Kifle, Decker, Wolfram, Fieker, Claus, Steenpass, Andreas   +3 more
core   +1 more source

Right triangles with algebraic sides and elliptic curves over number fields [PDF]

, 2009
Given any positive integer n, we prove the existence of infinitely many right triangles with area n and side lengths in certain number fields. This generalizes the famous congruent number problem.
Girondo, Ernesto, Gonzalez-Diez, Gabino, Gonzalez-Jimenez, Enrique, Steuding, Jorn, Steuding, Rasa   +4 more
core   +3 more sources

The polylogarithm in algebraic number fields

Journal of Number Theory, 1985
AbstractBased on Kummer's 2-variable functional equations for the second through fifth orders of the polylogarithm function, certain linear combinations, with rational coefficients, of polylogarithms of powers of an algebraic base were discovered to possess significant mathematical properties. These combinations are designated “ladders,” and it is here
M.D. Abouzahra, L. Lewin
openaire   +2 more sources

Splitting full matrix algebras over algebraic number fields

, 2011
Let K be an algebraic number field of degree d and discriminant D over Q. Let A be an associative algebra over K given by structure constants such that A is isomorphic to the algebra M_n(K) of n by n matrices over K for some positive integer n.
Acciaro, Babai, Bremner, Buchmann, Cassels, Chistov, Cohen, Cremona, Cremona, Cremona, Cremona, de Graaf, de Graaf, Eberly, Eberly, Eberly, Eberly, Fisher, Gábor Ivanyos, Hollanti, Ivanyos, Ivanyos, Ivanyos, Ivanyos, Ivanyos, Jacobson, Janusz, Josef Schicho, Kannan, Lajos Rónyai, Lenstra, Lenstra, Matoušek, Nebe, Pan, Pierce, Pílniková, Reiner, Rónyai, Rónyai, Rónyai, Rónyai, Sethuraman, Simon   +43 more
core   +1 more source

Analytic curves in algebraic varieties over number fields

, 2007
We establish algebraicity criteria for formal germs of curves in algebraic varieties over number fields and apply them to derive a rationality criterion for formal germs of functions, which extends the classical rationality theorems of Borel-Dwork and P\'
A Franchetta, B Dwork, C P Ramanujam, D G Cantor, D Harbater, D Mumford, D V Chudnovsky, D V Chudnovsky, E Kani, G Eisenstein, G Pólya, H Hironaka, H Hironaka, H Matsumura, H Randriambololona, J Fresnel, J.-B. Bost, J.-B. Bost, J.-B. Bost, J.-B. Bost, J.-P. Serre, L Bădescu, L Moret-Bailly, L Moret-Bailly, M Raynaud, M van der Put, P Graftieaux, P Graftieaux, R Hartshorne, R Hartshorne, R Rumely, R S Rumely, S Bosch, S Bosch, S Bosch, V G Berkovich, W Gubler, Y Amice, Y André, Y Ihara, Yu. I. Manin, É Borel   +41 more
core   +5 more sources

Modeling net ecosystem carbon balance and loss in coastal wetlands exposed to sea‐level rise and saltwater intrusion

Ecological Applications, Volume 32, Issue 8, December 2022., 2022
Abstract Coastal wetlands are globally important stores of carbon (C). However, accelerated sea‐level rise (SLR), increased saltwater intrusion, and modified freshwater discharge can contribute to the collapse of peat marshes, converting coastal peatlands into open water.
Khandker S. Ishtiaq, Tiffany G. Troxler, Lukas Lamb‐Wotton, Benjamin J. Wilson, Sean P. Charles, Stephen E. Davis, John S. Kominoski, David T. Rudnick, Fred H. Sklar   +8 more
wiley   +1 more source