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Date: 2015
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1197906
Description: We obtain a conditional, under the Generalized Riemann Hypothesis, lower bound on the number of distinct elliptic curves E over a prime finite field Fp of p elements, such that the discriminant D(E) o ... More
Reviewed: Reviewed
Date: 2015
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195893
Description: 13 page(s)
Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1194946
Description: Recently, several bounds have been obtained on the number of solutions of congruences of the type (x1+s)⋯(xv+s)≡(y1+s)⋯(yv+s)≢0 (mod p), where p is prime and variables take values in some short inter ... More
Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/324810
Description: We study polynomials with integer coefficients which become Eisenstein polynomials after the additive shift of a variable. We call such polynomials shifted Eisenstein polynomials. We determine an uppe ... More
Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1197832
Description: 13 page(s)
Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1197920
Description: 10 page(s)
Reviewed: Reviewed
Date: 2013
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/272190
Description: We obtain upper bounds on the number of solutions to congruences of the type (x1 + s)... (xv + s) ≡ (y1 + s)... (xv + s) ≢ 0 (mod p) modulo a prime p with variables from some short intervals. We give ... More
Reviewed: Reviewed
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/1959.14/231936
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/1959.14/221905
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: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/205033
Description: For a polynomial f∈Fp[X] , we obtain upper bounds on the number of points (x, f (x)) modulo a prime p which belong to an arbitrary square with the side length H. Our results in particular are based on ... 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: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/130338
Description: We give explicit formulas for the number of distinct elliptic curves over a finite field (up to isomorphism over the algebraic closure of the ground field) in several families of curves of cryptograph ... More
Reviewed: Reviewed
Date: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/130893
Description: Dynamical systems generated by iterations of multivariate polynomials with slow degree growth have proved to admit good estimates of exponential sums along their orbits which in turn lead to rather st ... More
Reviewed: Reviewed
Date: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/128917
Description: We study the distribution of singular and unimodular matrices in sumsets in matrix rings over finite fields. We apply these results to estimate the largest prime divisor of the determinants in sumsets ... More
Reviewed: Reviewed