Publications related to Prime number

Some consequences of Masser's counting theorem on elliptic curves

We use Masser's counting theorem to prove a lower bound for the canonical height in powers of elliptic curves. We also prove the Galois case of the elliptic Lehmer problem, combining Kummer theory and Masser's result with bounds on the rank and torsion of ...

Springer Heidelberg2017

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

Computation of a 768-Bit Prime Field Discrete Logarithm

Arjen Lenstra, Thorsten Kleinjung

This paper reports on the number field sieve computation of a 768-bit prime field discrete logarithm, describes the different parameter optimizations and resulting algorithmic changes compared to the factorization of a 768-bit RSA modulus, and briefly disc ...

Springer International Publishing Ag2017

On Moments Of Twisted L-Functions

Philippe Michel

We study the average of the product of the central values of two L-functions of modular forms f and g twisted by Dirichlet characters to a large prime modulus q. As our principal tools, we use spectral theory to develop bounds on averages of shifted convol ...

Johns Hopkins Univ Press2017

Combinatorial Algorithm for Restricted Max-Min Fair Allocation

Ola Nils Anders Svensson, Christos Kalaitzis, Chidambaram Annamalai

We study the basic allocation problem of assigning resources to players to maximize fairness. This is one of the few natural problems that enjoys the intriguing status of having a better estimation algorithm than approximation algorithm. Indeed, a certain ...

Association for Computing Machinery2017

Contextualizing the co-creation of artefacts within the nested social structure of a collaborative MOOC

Pierre Dillenbourg, Kshitij Sharma, Stian Haklev

MOOCs have traditionally been seen as providing an individual learning experience, however there is an increasing trend towards enabling social learning in MOOCs. To make online learning at scale more social and collaborative, some MOOCs have introduced co ...

2017

Computational Aspects of Jacobians of Hyperelliptic Curves

Alina Dudeanu

Nowadays, one area of research in cryptanalysis is solving the Discrete Logarithm Problem (DLP) in finite groups whose group representation is not yet exploited. For such groups, the best one can do is using a generic method to attack the DLP, the fastest ...

EPFL2016

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

Robert Granger, Thorsten Kleinjung, Jens Markus Zumbrägel

For~

q

a prime power, the discrete logarithm problem (DLP) in~

\F_{q}

consists in finding, for any

g \in \mathbb{F}_{q}^{\times}

and

h \in \langle g \rangle

, an integer~

x

such that

g^x = h

. We present an algorithm for computing discrete logarithm ...

2016

Sign changes of Kloosterman sums with almost prime moduli

Ping Xi

We prove that the Kloosterman sum changes sign infinitely often as runs over squarefree moduli with at most 10 prime factors, which improves the previous results of Fouvry and Michel, Sivak-Fischler and Matomaki, replacing 10 by 23, 18 and 15, respectively ...

Springer Verlag2015

On The Exponent Of Distribution Of The Ternary Divisor Function

Philippe Michel

We show that the exponent of distribution of the ternary divisor function d(3) in arithmetic progressions to prime moduli is at least 1/2 + 1/46, improving results of Friedlander-Iwaniec and Heath-Brown. Furthermore, when averaging over a fixed residue cla ...

London Mathematical Society, Cambridge2015

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Some consequences of Masser's counting theorem on elliptic curves

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

Computation of a 768-Bit Prime Field Discrete Logarithm

On Moments Of Twisted L-Functions

Combinatorial Algorithm for Restricted Max-Min Fair Allocation

Contextualizing the co-creation of artefacts within the nested social structure of a collaborative MOOC

Computational Aspects of Jacobians of Hyperelliptic Curves

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

Sign changes of Kloosterman sums with almost prime moduli

On The Exponent Of Distribution Of The Ternary Divisor Function

Combinatorial Algorithm for Restricted Max-Min Fair Allocation

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

Computation of a 768-Bit Prime Field Discrete Logarithm

Some consequences of Masser's counting theorem on elliptic curves

Contextualizing the co-creation of artefacts within the nested social structure of a collaborative MOOC

On Moments Of Twisted L-Functions

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

Computational Aspects of Jacobians of Hyperelliptic Curves

Sign changes of Kloosterman sums with almost prime moduli

On The Exponent Of Distribution Of The Ternary Divisor Function