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Concept

Perfect number

Related publications (9)

Coherent actions by homeomorphisms on the real line or an interval

Yash Lodha

We study actions of groups by orientation preserving homeomorphisms on R (or an interval) that are minimal, have solvable germs at +/-infinity and contain a pair of elements of a certain dynamical type. We call such actions coherent. We establish that such ...

HEBREW UNIV MAGNES PRESS2020

Incidences between points and generalized spheres over finite fields and related problems

Van Thang Pham

Let F-q be a finite field of q elements, where q is a large odd prime power and Q = a(1)x(1)(c1) + ..... + a(d)x(d)(cd) is an element of F-q[x(1) ,...,x(d)], where 2

Walter De Gruyter Gmbh2017

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

Faster ECC over $\mathbb{F}_{2^{521}-1}$

Robert Granger

In this paper we present a new multiplication algorithm for residues modulo the Mersenne prime

2^{521}−1

. Using this approach, on an Intel Haswell Core i7-4770, constant-time variable-base scalar multiplication on NIST’s (and SECG’s) curve P-521 requires ...

Springer Berlin Heidelberg2015

Upper bounds for the Euclidean minima of abelian fields of odd prime power conductor

Eva Bayer Fluckiger

The aim of this paper is to give upper bounds for the Euclidean minima of abelian fields of odd prime power conductor. In particular, these bounds imply Minkowski's conjecture for totally real number fields of conductor p(r), where p is an odd prime number ...

Springer Verlag2013

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

Adjacent Crossings Do Matter

Radoslav Fulek

In a drawing of a graph, two edges form an odd pair if they cross each other an odd number of times. A pair of edges is independent if they share no endpoint. For a graph G, let ocr(G) be the smallest number of odd pairs in a drawing of G and let iocr(G) b ...

Springer-Verlag Berlin2011

Piercing Quasi-Rectangles: On a Problem of Danzer and Rogers

János Pach

It is an old problem of Danzer and Rogers to decide whether it is possible arrange O(1/epsilon) points in the unit square so that every rectangle of area epsilon contains at least one of them. We show that the answer to this question is in the negative if ...