Add to Quick Collection All 373 Results

Add All Items to Quick Collection

**Date:** 2004
**Subject Keyword:**
010100 Pure Mathematics
| repeated powering
| cycle structure
| primes in arithmetic progressions
**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:**
**Date:** 2010
**Subject Keyword:**
010100 Pure Mathematics
| rank of elliptic curve
| function field
| multiplicative order
**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:**
**Date:** 2012
**Subject Keyword:**
080200 Computation Theory and Mathematics
| Elliptic curves
| Embedding degree
| MNT curves
| Pairing based cryptography
**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:**
**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:**
**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
**Full Text:**
**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:**
**Date:** 2010
**Language:** eng
**Resource Type:** journal article
**Identifier:** http://hdl.handle.net/1959.14/128904
**Description:**
9 page(s)
**Reviewed:**
**Authors:**
Shparlinski, Igor E
**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:**
**Date:** 2006
**Subject Keyword:**
010100 Pure Mathematics
| pseudorandom numbers
| nonlinear congruential method
| discrepancy
| exponential sums
**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:**
**Date:** 2007
**Subject Keyword:**
010100 Pure Mathematics
| special sequences and polynomials
| higher degree equations
| Fermat's equation
| applications of sieve methods
**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
**Full Text:**
**Reviewed:**
**Date:** 2009
**Subject Keyword:**
010100 Pure Mathematics
| 080200 Computation Theory and Mathematics
| graph spectrum
| integral eigenvalue
| random matrix
| Cayley graph
**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:**
**Date:** 2009
**Subject Keyword:**
080200 Computation Theory and Mathematics
| Pseudorandom numbers
| Artin's conjecture
| primes in arithmetic progressions
**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:**
**Reviewed:**
**Date:** 2009
**Subject Keyword:**
080200 Computation Theory and Mathematics
**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
**Authors:**
Shparlinski, Igor E
**Date:** 2014
**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:**
**Date:** 2007
**Subject Keyword:**
080200 Computation Theory and Mathematics
| public key cryptography
| elliptic curves
| Koblitz curves
| character sums
| pseudorandomness
**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:**

Copyright Macquarie University | Privacy Statement | Accessibility Information

ABN 90 952 801 237 | CRICOS Provider No 00002J