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Date: 2004
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/118689
Description: In a recent work, Shallit and Vasiga have obtained several results about tails and cycles in orbits of repeated squaring. Some of these results have been based on the Extended Riemann Hypothesis. Here ... More
Reviewed: Reviewed
Date: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/129099
Description: We show that the average and typical ranks in a certain parametric family of elliptic curves described by D. Ulmer tend to infinity as the parameter d - ∞. This is perhaps unexpected since by a result ... More
Reviewed: Reviewed
Date: 2012
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/172505
Description: We give an upper bound on the number of finite fields over which elliptic curves of cryptographic interest with a given embedding degree and small complex multiplication discriminant may exist, and pr ... More
Full Text: Full Text
Reviewed: Reviewed
Date: 2012
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/176439
Description: We recall that a polynomial f(X)= K[X] over a field K is called stable if all its iterates are irreducible over K. We show that almost all monic quadratic polynomials f(X) = ℤ[X] are stable over ℚ. We ... More
Reviewed: Reviewed
Date: 2010
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/125252
Description: We use the Weil bound of multiplicative character sums, together with some recent results of N. Boston and R. Jones, to show that the critical orbit of quadratic polynomials over a finite field of q e ... More
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Reviewed: Reviewed
Date: 2016
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/1197843
Description: We use the theory of exponent pairs and Vaaler polynomials to show that any interval of the form [x,x+x¹/²] contains an integral multiple m²r ∈ [x,x+x¹/²] of a perfect square m² with an integer m > x⁰ ... More
Reviewed: Reviewed
Date: 2010
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/128904
Description: 9 page(s)
Reviewed: Reviewed
Date: 2004
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/118634
Description: 7 page(s)
Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/9952
Description: The nonlinear congruential method is an attractive alternative to the classical linear congruential method for pseudorandom number generation. In this paper we present a new bound on the s-dimensional ... More
Reviewed: Reviewed
Date: 2007
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/43355
Description: In this note, we show that if we write ⌊en!⌋ = s(n)u(n)², where s(n) is square-free then [equation ommitted due to formatting reasons] has at least C log logN distinct prime factors for some absolute ... More
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Reviewed: Reviewed
Date: 2009
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/129659
Description: It is shown that only a fraction of 2-Ω(n) of the graphs on n vertices have an integral spectrum. Although there are several explicit constructions of such graphs, no upper bound for their number has ... More
Reviewed: Reviewed
Date: 2009
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/132977
Description: We show, under the Generalized Riemann Hypothesis, that a certain set of primes which is of importance for the theory of pseudorandom sequences is of positive relative density. We also use an uncondit ... More
Full Text: Full Text
Reviewed: Reviewed
Date: 2009
Language: eng
Resource Type: book chapter
Identifier: http://hdl.handle.net/1959.14/92393
Description: It has been shown by J.-P. Serre that the largest possible number of Fq-rational points on curves of small genus over the finite field Fq of q elements depends on the divisibility property p | [2q½], ... More
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: 2007
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/41852
Description: We estimate character sums over points on elliptic curves over a finite field Fq of q elements. Pseudorandom sequences can be constructed by taking linear combinations with small coefficients (for exa ... More
Reviewed: Reviewed