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Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/334261
Description: Let V be a fixed algebraic variety defined by m polynomials in n variables with integer coefficients. We show that there exists a constant C(V) such that for almost all primes p for all but at most C( ... More
Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/332051
Description: Let Fq be a finite field of q elements. E. Howe has shown that there is a natural correspondence between the isogeny classes of two-dimensional ordinary abelian varieties over Fq which do not contain ... More
Reviewed: Reviewed
Date: 2014
Subject Keyword: Evasiveness | Sparse graphs | Prime numbers
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/332105
Description: We give an unconditional version of a conditional, on the Extended Riemann Hypothesis, result of Babai, Banerjee, Kulkarni and Naik (2010) [1] on the evasiveness of sparse graphs on n nodes, provided ... More
Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1194586
Description: We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. We use this bound to improve a series of previous results on various exponential sums and some arithm ... More
Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195859
Description: We consider a modification of the noisy polynomial interpolation problem of recovering an unknown f(X) ∈ ℤ [X] polynomial from approximate values of the residues of f(t) modulo a prime p at polynomial ... More
Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1197903
Description: We obtain new bounds of multivariate exponential sums with monomials, when the variables run over rather short intervals. Furthermore, we use the same method to derive estimates on similar sums with m ... More
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/1959.14/339382
Description: D. Gómez-Pérez, A. Ostafe, A.P. Nicol-Las and D. Sadornil have recently shown that for almost all polynomials f ∈ Fq[X] over the finite field of q elements, where q is an odd prime power, their iterat ... 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/1959.14/331872
Description: We use bounds of mixed character sum to study the distribution of solutions to certain polynomial systems of congruences modulo a prime p. In particular, we obtain nontrivial results about the number ... More
Full Text: Full Text
Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/332383
Description: We give an upper bound for the number of elliptic Carmichael numbers η ≤ χ that were recently introduced by J. H. Silverman in the case of an elliptic curve without complex multiplication (non CM). We ... 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/1959.14/332390
Description: 10 page(s)
Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195015
Description: 32 page(s)
Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/328486
Description: Motivated by some algorithmic applications, we obtain upper bounds on the number of solutions of the equation x₁...xn = λ with variables x₁, . . ., xn from a low-dimensional affine space in a high deg ... More
Reviewed: Reviewed