https://ogma.newcastle.edu.au/vital/access/ /manager/Index ${session.getAttribute("locale")} 5 https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:30912 r₁,..., r_s: Z_n≥0 → C be linearly recurrent sequences whose associated eigenvalues have arguments in πQ and let F(z) := Σ_n ≥ 0 f(n)zn, where f(n) ∈ {r1(n),..., rs(n)} for each n ≥ 0. We prove that if F(z) is bounded in a sector of its disk of convergence, then it is a rational function. This extends a very recent result of Tang and Wang, who gave the analogous result when the sequence f(n) takes on values of finitely many polynomials.]]> Wed 11 Apr 2018 16:49:35 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:40110 Thu 28 Jul 2022 15:35:25 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:28086 m for each positive integer m, the set of points {(n, 2ⁿ mod 3^m): n = 0}, viewed as a subset of Z=0 ×Z=0 is bi-periodic, with minimal periods f(3^m) (horizontally) and 3^m (vertically). We show that if one considers the classes of n modulo 6, one obtains a finer structural classification. This result is presented within the context of the question of strong normality of Stoneham numbers.]]> Sat 24 Mar 2018 07:39:48 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:28706 n has no proper Hadamard submatrix of order m > n/2. We generalize this result to maximal determinant submatrices of Hadamard matrices, and show that an interval of length ~ n/2 is excluded from the allowable orders. We make a conjecture regarding a lower bound for sums of squares of minors of maximal determinant matrices, and give evidence to support it. We give tables of the values taken by the minors of all maximal determinant matrices of orders ≤ 21 and make some observations on the data. Finally, we describe the algorithms that were used to compute the tables.]]> Sat 24 Mar 2018 07:30:08 AEDT ]]>