We prove an asymptotic formula for the shifted convolution of the divisor functions d(k)(n) and d(n) with k >= 4, which is uniform in the shift parameter and which has a power saving error term, improving results obtained previously by Fouvry and Tenenbaum ...
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 ...
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 ...
We establish estimates for the number of solutions of certain affine congruences. These estimates are then used to prove Manin's conjecture for a cubic surface split over Q whose singularity type is D-4. This improves on a result of Browning and answers a ...
We show that, in a restricted range, the divisor function of integers in residue classes modulo a prime follows a Gaussian distribution, and a similar result for Hecke eigenvalues of classical holomorphic cusp forms. Furthermore, we obtain the joint distri ...
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 ...
We present the first model-independent measurement of the absolute branching fraction of the Lambda(+)(c) -> pK(-)pi(+)decay using a data sample of 978 fb(-1) collected with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. The number of ...
We consider the problem of reaching agreement in distributed systems in which some processes may deviate from their prescribed behavior before they eventually crash. We call this failure model "mortal Byzantine". After discussing some application examples ...
Nowadays, the most popular public-key cryptosystems are based on either the integer factorization or the discrete logarithm problem. The feasibility of solving these mathematical problems in practice is studied and techniques are presented to speed-up the ...
We show that the prime divisors of a random polynomial in F-q[t] are typically "Poisson distributed". This result is analogous to the result in Z of Granville [1]. Along the way, we use a sieve developed by Granville and Soundararajan [2] to give a simple ...
