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Date: 2013
Language: eng
Resource Type: book chapter
Identifier: http://hdl.handle.net/1959.14/224276
Description: We present a collection of several natural questions about elliptic curves, mostly over finite fields, that have led to some interesting number theoretic questions and whose solutions require rather i ... More
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/271249
Description: We show that for any integers a and m with m ≥ 1 and gcd(a,m) = 1, there is a solution to the congruence pr ≡ a (modm) where p is prime, r is a product of at most k = 17 prime factors and p, r ≤ m. Th ... More
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/276005
Description: We obtain an asymptotic formula for the number of square-free integers in N consecutive values of polynomials on average over integral polynomials of degree at most k and of height at most H, where H ... More
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/221895
Description: 11 page(s)
Reviewed: Reviewed
Date: 2013
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/221888
Description: 8 page(s)
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/231936
Description: We obtain a more precise version of an asymptotic formula of A. Dubickas for the number of monic Eisenstein polynomials of fixed degree d and of height at most H, as H → ∞. In particular, we give an e ... More
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/221582
Description: 32 page(s)
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/221905
Description: We study the security of the linear generator over a finite field. It is shown that the seed of a linear generator can be deduced from partial information of a short sequence of consecutive outputs of ... More
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/272100
Description: We present some theoretical bounds and algorithms concerning the statistics of different reduction types in the family of Fermat curves Yp = Xs(1 - X ), where p is prime and s = 1,..., p - 2.
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/202794
Description: We give a survey of a variety of recent results about the distribution and some geometric properties of points (x, y) on modular hyperbolas xy ≡ a (mod m). We also outline a very diverse range of appl ... More
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/173573
Description: We estimate multiplicative character sums over the integers with a fixed sum of binary digits and apply these results to study the distribution of products of such integers in residues modulo a prime ... More
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/172365
Description: We give an upper bound on the number of vertices of the convex hull of the set of solutions to multivariate polynomial congruences modulo a prime p. The result is based on a combination of an estimate ... More
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/198238
Description: We use a result of É. Fouvry about the distribution of solutions to systems of congruences with multivariate polynomials in small cubic boxes and some ideas of W. Schmidt to derive an asymptotic formu ... More
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: conference paper
Identifier: http://hdl.handle.net/1959.14/183072
Description: 14 page(s)
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/218019
Description: We obtain several versions of the sum-product theorem with k-fold sums and product sets. We also give several applications of these estimates.
Reviewed: Reviewed