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Statistics Of Prime Divisors In Function Fields

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On the scaling of polar codes: II. The behavior of un-polarized channels

Rüdiger Urbanke, Seyed Hamed Hassani

We provide upper and lower bounds on the escape rate of the Bhattacharyya process corresponding to polar codes where transmission takes place over the the binary erasure channel. More precisely, we bound the exponent of the number of sub-channels whose Bha ...

IEEE2010

2-Selmer groups and the Birch-Swinnerton-Dyer Conjecture for the congruent number curves

Robert Christopher Rhoades

We take an approach toward Counting the number of integers n for which the curve (n),: y(2) = x(3) - n(2)x has 2-Selmer groups of a given size. This question was also discussed in a pair of papers by Roger Heath-Brown. In contrast to earlier work, our anal ...

2009

Le carré de la fonction des diviseurs

Nicolas Bersier

Let d(n) denote Dirichlet's divisor function for positive integer numbers. This work is primarily concerned with the study of We are interested, in the error term where Ρ3 is a polynomial of degree 3 ; more precisely xΡ3(log x) is the residue of in s = 1. ...

EPFL2007

A kilobit special number field sieve factorization

Arjen Lenstra, Thorsten Kleinjung, Dag Arne Osvik

We describe how we reached a new factoring milestone by completing the first special number field sieve factorization of a number having more than 1024 bits, namely the Mersenne number 21039 -1. Although this factorization is orders of magnitude ...

2007

Primality Testing

Kamal Tahiri Jouti

Since the discovery of the utility of the numbers, the human being tried to differentiate them. We decide between them according to whether they are even or odd. Or, according to the fact that they are prime or composite. A natural number n >1 is called a ...

2006

Search for lepton and baryon number violating τ- decays into Λ̄π- and Λπ-

Olivier Schneider, Stewart Cole, Chao Wang, Tagir Aushev, Lei Zhang, Vladislav Balagura, Sun Hee Kim, Ji Hyun Kim

We have searched for τ lepton decays, τ-→Λ̄π- and τ-→Λπ-, that simultaneously violate the conservation of the lepton (L) and baryon (B) number using a data sample of 154 fb-1 collected with the Belle detector at the KEKB e+e- asymmetric-energy collider. No ...

2006

Phases of granular segregation in a binary mixture

Pedro Miguel Nunes Pereira de Almeida Reis

We present results from an extensive experimental investigation into granular segregation of a shallow binary mixture in which particles are driven by frictional interactions with the surface of a vibrating horizontal tray. Three distinct phases of the mix ...

2006

The Plenacoustic Function and its Sampling

Martin Vetterli, Luciano Sbaiz, Thibaut Ajdler

We study the spatialization of the sound field in a room, in particular the evolution of room impulse responses as a function of their spatial positions. We observe that the multidimensional spectrum of the solution of the wave equation has an almost bandl ...

2005

Hard equality constrained integer knapsacks

Arjen Lenstra

We consider the following integer feasibility problem: Given positive integer numbers a0, a1,&mellip;,an with gcd(a1,&mellip;,an) = 1 and a = (a1,&mellip;,an), does there exist a ...

2004

Function Field Sieve in Characteristic Three

Robert Granger

In this paper we investigate the efficiency of the function field sieve to compute discrete logarithms in the finite fields

\mathbb{F}_{3^n}

. Motivated by attacks on identity based encryption systems using supersingular elliptic curves, we pay special at ...

Springer Berlin Heidelberg2004

Function Field Sieve in Characteristic Three

Robert Granger

In this paper we investigate the efficiency of the function field sieve to compute discrete logarithms in the finite fields

\mathbb{F}_{3^n}

. Motivated by attacks on identity based encryption systems using supersingular elliptic curves, we pay special at ...

Springer Berlin Heidelberg2004