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Date: 2017
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1197769
Description: Given a polynomial g of positive degree over a finite field, we show that the proportion of polynomials of degree n, which can be written as h+gk, where h is an irreducible polynomial of degree n and ... More
Reviewed: Reviewed
Date: 2017
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1193205
Description: 8 page(s)
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195192
Description: We derive two new upper bounds on the double multiplicative character sum over subgroups and intervals Rχ(a,g,I,N)=∑x=1H|∑n=1Nχ(x+agⁿ)| where χ is a multiplicative character modulo a prime p, H and N ... More
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195166
Description: We consider various counting questions for irreducible binomials of the form Xt-a over finite fields. We use various results from analytic number theory to investigate these questions.
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195102
Description: We improve several recent results by Hong, Lee, Lee and Park (2012) on gaps and Bzdȩga (2014) on jumps amongst the coefficients of cyclotomic polynomials. Besides direct improvements, we also introduc ... More
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1055140
Description: Given a function f in a finite field Fq of q elements, we define the functional graph of f as a directed graph on q nodes labelled by the elements of Fq where there is an edge from u to v if and only ... More
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1193207
Description: We use character sums to derive new bounds on the additive energy of the set of distances (counted with multiplicities) between two subsets of a vector space over a given finite field. We also give ap ... More
Reviewed: Reviewed
Date: 2015
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1197318
Description: Given two sets A and B of integers, we consider the problem of finding a set S⊆A of the smallest possible cardinality such the greatest common divisor of the elements of S∪B equals that of those of A∪ ... More
Reviewed: Reviewed
Date: 2015
Subject Keyword: GCD | Approximate GCD
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195921
Description: 11 page(s)
Reviewed: Reviewed
Date: 2014
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/328476
Description: Motivated by a recent application to hash functions suggested by O. Chevassut, P.-A. Fouque, P. Gaudry and D. Pointcheval, we study the frequency with which groups of points on an elliptic curve over ... More
Reviewed: Reviewed
Date: 2014
Subject Keyword: Exponential function | Prime power
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1197896
Description: For a fixed integer g≥2, we consider the distribution of powers gⁿ in the residue ring modulo a large power of a fixed prime. We also give an application of this result to the exponential pseudorandom ... 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/1959.14/328486
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
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/221647
Description: 4 page(s)
Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/221396
Description: 12 page(s)
Reviewed: Reviewed