Results 291 to 300 of about 609,367 (341)

QFESTA: Efficient Algorithms and Parameters for FESTA using Quaternion Algebras

IACR Cryptology ePrint Archive, 2023
Kohei Nakagawa, Hiroshi Onuki
semanticscholar   +1 more source

Quaternion algebras, Heegner points and the arithmetic of Hida families

, 2009
Given a newform f, we extend Howard’s results on the variation of Heegner points in the Hida family of f to a general quaternionic setting. More precisely, we build big Heegner points and big Heegner classes in terms of compatible families of Heegner ...
M. Longo, S. Vigni
semanticscholar   +1 more source

NTRU in Quaternion Algebras of Bounded Discriminant

Post-Quantum Cryptography, 2023
Congli Ling, Andrew Mendelsohn
semanticscholar   +1 more source

On quaternion algebras

Journal of Mathematical Sciences, 1995
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Generalized quaternion algebras

Mathematical Notes, 1993
Es sei \(A\) ein kommutativer Ring, in dem 2 invertierbar ist. Zu invertierbaren Elementen \(a,b\in A\) sei \(Q=(a,b/A)\) die verallgemeinerte Quaternionenalgebra. Der Verf. zeigt, daß \(Q\) genau dann rechtsdistributiv ist, wenn \(A\) distributiv und die quadratische Form \(x^2-ay^2-bz^2\) nullteilig modulo jedem maximalen Ideal \(M\) von \(A\) ist ...
openaire   +1 more source

Algebras, Quaternions and Quaternionic Symplectic Groups

2002
In this chapter we begin by studying algebras over a field, with their groups of units providing many interesting groups. In particular, we study division algebras and their linear algebra. Then we introduce the quaternions which form the only non-commutative example of a real division algebra.
openaire   +1 more source

Orders in Quaternion Algebras

2003
The basic algebraic theory of quaternion algebras was given in Chapter 2. That sufficed for the results obtained so far on deducing information on a Kleinian group Γ from its invariant trace field kΓ and invariant quaternion algebra AΓ. We have yet to expound on the arithmetic theory of quaternion algebras over number fields.
Colin Maclachlan, Alan W. Reid
openaire   +1 more source

Levels of quaternion algebras

Archiv der Mathematik, 2008
The level of a ring R with 1 ≠ 0 is the smallest positive integer s such that −1 can be written as a sum of s squares in R, provided −1 is a sum of squares at all. D. W. Lewis showed that any value of type 2n or 2n + 1 can be realized as level of a quaternion algebra, and he asked whether there exist quaternion algebras whose levels are not of that ...
openaire   +1 more source

Intrinsic in-plane nodal chain and generalized quaternion charge protected nodal link in photonics

Light: Science and Applications, 2021
Dongyang Wang, Biao Yang, Qinghua Guo
exaly  

Non-Local Robust Quaternion Matrix Completion for Large-Scale Color Image and Video Inpainting

IEEE Transactions on Image Processing, 2022
Zhi-Gang Jia, Qiyu Jin, Michael Ng
exaly