Macquarie University, Sydney Macquarie University ResearchOnline

Showing items 1 - 15 of 47.

Add to Quick Collection   All 47 Results

Sort:
 Add All Items to Quick Collection
Date: 2006
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/14936
Description: The authors define the notion of 2-filtered 2-category and give an explicit construction of the bicolimit of a category valued 2-functor. A category considered as a trivial 2-category is 2-filtered if ... More
Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: book chapter
Identifier: http://hdl.handle.net/1959.14/8814
Description: 19 page(s)
Date: 2006
Language: eng
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.14/20581
Description: We show that if log(2 − Δ)f ∈ L²(ℝd), then the inverse Fourier transform of f converges almost everywhere. Here the partial integrals in the Fourier inversion formula come from dilates of a closed bou ... More
Reviewed: Reviewed
Date: 2006
Language: eng
Resource Type: book chapter
Identifier: http://hdl.handle.net/1959.14/10823
Description: 36 page(s)
Date: 2006
Language: eng
Resource Type: book chapter
Identifier: http://hdl.handle.net/1959.14/7623
Description: 33 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
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
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
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: conference paper
Identifier: http://hdl.handle.net/1959.14/103684
Description: In this report I sanitise (in the sense of ‘bring some sanity to’) the arguments of earlier reports detailing the correspondence between sequences (M+hS)–∞<h<∞ of divisors on elliptic and genus two hy ... More
Reviewed: Reviewed
Date: 2006
Subject Keyword: 010100 Pure Mathematics
Language: eng
Resource Type: conference paper
Identifier: http://hdl.handle.net/1959.14/1155037
Description: 23 page(s)
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