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Date: 2006
Language: eng
Resource Type: conference paper
Identifier: http://hdl.handle.net/1959.14/124379
Description: 9 page(s)
Date: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/20103
Description: We study some arithmetic properties of the Ramanujan function τ(n), such as the largest prime divisor P(τ(n)) and the number of distinct prime divisors ω(τ(n)) of τ(n) for various sequences of n. In p ... More
Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/15826
Description: For a positive integer n, we let φ(n) and λ(n) denote the Euler function and the Carmichael function, respectively. We define ξ(n) as the ratio φ(n)/λ(n) and study various arithmetic properties of ξ(n ... More
Reviewed: Reviewed
Date: 2006
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/20350
Description: We study values of the Euler function ϕ(n) taken on binary palindromes of even length. In particular, if B₂l denotes the set of binary palindromes with precisely 2l binary digits, we derive an asympto ... More
Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/9957
Description: We estimate character sums with Catalan numbers and middle binomial coefficients modulo a prime p. We use this bound to show that the first at most p<sup>13/2</sup>(logp)⁶ elements of each sequence al ... More
Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/13401
Description: We obtain upper bounds on character sums and autocorrelation of nonlinear recurrence sequences over arbitrary finite rings.
Reviewed: Reviewed
Date: 2006
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/20134
Description: We give nontrivial bounds in various ranges for exponential sums of the form [equation omitted for formatting reasons] and [equation omitted for formatting reasons] where m ≥ 2, ϑ is an element of ord ... More
Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/9972
Description: Let φ denote the Euler function. For a fixed integer k ≠ 0, we study positive integers n for which the largest prime factor of φ(n) also divides φ(n + k). We obtain an unconditional upper bound on the ... 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: 2006
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/20349
Description: We give upper bounds for the number of solutions to congruences with the Euler function ϕ(n) modulo an integer q ≥ 2. We also give nontrivial bounds for rational exponential sums with ϕ(n)/q.
Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: conference paper
Identifier: http://hdl.handle.net/1959.14/9989
Description: We construct systems of bases of ℂ<sup>n</sup> which are mutually almost orthogonal and which might turn out to be useful for quantum computation. Our constructions are based on bounds of classical ex ... More
Reviewed: Reviewed
Date: 2006
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/20094
Description: For a fixed integer s ≥ 1, we estimate exponential sums with harmonic sums [equation omitted for formatting reasons] individually and on average, where Hs (n) is computed modulo a prime p. These bound ... More
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: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/20158
Description: We estimate certain double character sums over points of an elliptic curve and in the multiplicative subgroup of a finite field. These bounds both improve and extend the scope of a series of previous ... More
Reviewed: Reviewed