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Date: 2011
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/163352
Description: We estimate the number of possible degree patterns of k-lacunary polynomials of degree t<p which split completely modulo p. The result is based on a combination of a bound on the number of zeros of la ... More
Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/20160
Description: We use bounds of exponential sums to derive new lower bounds on the number of distinct distances between all pairs of points (x,y) ∈ A×B for two given sets A,B ∈ Fnq, where Fq is a finite field of q e ... More
Full Text: Full Text
Reviewed: Reviewed
Date: 2008
Language: eng
Resource Type: conference proceedings editorship
Identifier: http://hdl.handle.net/1959.14/1251921
Description: 265 page(s)
Date: 2008
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1244068
Description: 7 page(s)
Reviewed: Reviewed
Date: 2008
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/81856
Description: We obtain upper and lower bounds on the average energy of circulant graphs with n vertices and regularity d. The average is taken over all representations of such graphs by circulant adjacency matrice ... More
Reviewed: Reviewed
Date: 2009
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/145345
Description: We study the hash function from a finite field Fq into an elliptic curve over Fq which has recently been introduced by T. Icart. In particular we slightly adjust and prove the asymptotic formula conje ... More
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Reviewed: Reviewed
Date: 2013
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/221564
Description: At Crypto 2010, Brier et al. proposed the first construction of a hash function into ordinary elliptic curves that was indifferentiable from a random oracle, based on Icart's deterministic encoding fr ... More
Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/43466
Description: Given an integer n, how hard is it to find the set of all integers m such that φ(m) = n, where φ is the Euler totient function? We present a certain basic algorithm which, given the prime number facto ... More
Full Text: Full Text
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: 2000
Language: eng
Resource Type: conference paper
Identifier: http://hdl.handle.net/1959.14/1233606
Description: 10 page(s)
Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1195121
Description: There is a well-known asymptotic formula, due to W. M. Schmidt [Duke Math. J., 35 (1968), pp. 327-339], for the number of full-rank integer lattices of index at most V in ℤⁿ. This set of lattices L ca ... More
Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/9947
Description: Miyaji, Nakabayashi and Takano have recently suggested a construction of the so-called MNT elliptic curves with low embedding degree, which are also of importance for pairing-based cryptography. We gi ... More
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: 2008
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/81867
Description: In this paper we give upper and lower bounds as well as a heuristic estimate on the number of vertices of the convex closure of the set Gn = {(a, b) : a, b ∈ ℤ, ab ≡ 1 (mod n) , 1 ≤ a, b ≤ n - 1} . Th ... More
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