Concept

Nombre double de Mersenne

Publications associées (19)

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The double exponential runtime is tight for 2-stage stochastic ILPs

Kim-Manuel Klein, Klaus Jansen, Alexandra Anna Lassota

We consider fundamental algorithmic number theoretic problems and their relation to a class of block structured Integer Linear Programs (ILPs) called 2-stage stochastic. A 2-stage stochastic ILP is an integer program of the form min{c(T)x vertical bar Ax = ...

SPRINGER HEIDELBERG2022

Universal p'-central extensions

Jacques Thévenaz, Caroline Lassueur

It is well-known that a finite group possesses a universal central extension if and only if it is a perfect group. Similarly, given a prime number p, we show that a finite group possesses a universal p′-central extension if and only if the p′-part of its a ...

Elsevier2017

Isogeny graphs of ordinary abelian varieties

Dimitar Petkov Jetchev, Benjamin Pierre Charles Wesolowski, Ernest Hunter Brooks

Fix a prime number l. Graphs of isogenies of degree a power of l are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the case of absolutely simple ordinary abelian varieties over a finite field. We analyse gr ...

Springer Heidelberg2017

Prime Power Terms In Elliptic Divisibility Sequences

Valéry Aurélien Mahé

We study a problem on specializations of multiples of rational points on elliptic curves analogous to the Mersenne problem. We solve this problem when descent via isogeny is possible by giving explicit bounds on the indices of prime power terms in elliptic ...

American Mathematical Society2014

Generalised Mersenne Numbers Revisited

Robert Granger

Generalised Mersenne Numbers (GMNs) were defined by Solinas in 1999 and feature in the NIST (FIPS 186-2) and SECG standards for use in elliptic curve cryptography. Their form is such that modular reduction is extremely efficient, thus making them an attrac ...

2013

The functor of p-permutation modules for abelian groups

Mélanie Baumann

Let k be a field of characteristic p, where p is a prime number, let pp_k(G) be the Grothendieck group of p-permutation kG-modules, where G is a finite group, and let Cpp_k(G) be pp_k(G) tensored with the field of complex numbers C. In this article, we fin ...

Elsevier2013

Le foncteur de bi-ensembles des modules de p-permutation

Mélanie Baumann

Let k be an algebraically closed field of characteristic p, where p is a prime number or 0. Let G be a finite group and ppk(G) be the Grothendieck group of p-permutation kG-modules. If we tensor it with C, then Cppk becomes a C-linear biset functor. Recall ...

EPFL2012

Relative Projectivity and Relative Endotrivial Modules

Caroline Lassueur

This dissertation is concerned with modular representation theory of finite groups, and more precisely, with the study of classes of representations, which we shall term relative endotrivial modules. Given a prime number p, a finite group G of order divisi ...

EPFL2012

Efficient SIMD arithmetic modulo a Mersenne number

Arjen Lenstra, Joppe Willem Bos, Thorsten Kleinjung

This paper describes carry-less arithmetic operations modulo an integer 2^M − 1 in the thousand-bit range, targeted at single instruction multiple data platforms and applications where overall throughput is the main performance criterion. Using an implemen ...

IEEE Computer Soc Press2011

Efficient SIMD Arithmetic Modulo a Mersenne Number

Arjen Lenstra, Joppe Willem Bos, Thorsten Kleinjung

This paper describes carry-less arithmetic operations modulo an integer 2^M-1 in the thousand-bit range, targeted at single instruction multiple data platforms and applications where overall throughput is the main performance criterion. Using an implementa ...

IEEE2011