Auxiliary polynomials for some problems regarding Mahler’s measure (2009)
Artūras Dubickas, J. Mossinghoff
Abstract. We describe an iterative method of constructing some favorable auxiliary polynomials used to obtain lower bounds in some problems of algebraic number theory. With this method we improve a...
MATHEMATICS OF COMPUTATION S 0025-5718(09)02211-X (2009)
Lower Bounds, For Z-numbers, Artūras Dubickas, J. Mossinghoff
Abstract. Let p/q be a rational noninteger number with p>q ≥ 2. A real number λ>0isaZ p/q-number if {λ(p/q) n} < 1/q for every nonnegative integer n, where{x} denotes the fractional part...
LOWER BOUNDS FOR Z-NUMBERS (2008)
Artūras Dubickas, J. Mossinghoff
Abstract. Let p/q be a rational noninteger number with p> q ≥ 2. A real number λ> 0 is a Z p/q-number if {λ(p/q) n} < 1/q for every nonnegative integer n, where {x} denotes the...
Small limit points of Mahler’s measure (2008)
Abstract. Let M(P (z1,..., zn)) denote Mahler’s measure of the polynomial P (z1,..., zn). Measures of polynomials in n variables arise naturally as limiting values of measures of polynomials in...
SIGN CHANGES IN SUMS OF THE LIOUVILLE FUNCTION (2008)
Peter Borwein, Ron Ferguson, J. Mossinghoff
Abstract. The Liouville function λ(n) is the completely multiplicative function whose value is −1 at each prime. We develop some algorithms for computing the sum T (n) = Pn k=1 λ(k)/k, and use...
SIGN CHANGES IN SUMS OF THE LIOUVILLE FUNCTION (2008)
Peter Borwein, Ron Ferguson, J. Mossinghoff
Abstract. The Liouville function λ(n) is the completely multiplicative function whose value is −1 at each prime. We develop some algorithms for computing the sum T (n) = Pn k=1 λ(k)/k, and use...
Newman polynomials with prescribed vanishing and integer sets with distinct subset sums (2008)
Abstract. We study the problem of determining the minimal degree d(m) of a polynomial that has all coefficients in {0, 1} and a zero of multiplicity m at −1. We show that a greedy solution is...
TRACEABILITY IN SMALL CLAW-FREE GRAPHS (2008)
John M. Harris, J. Mossinghoff
Abstract. We prove that a claw-free, 2-connected graph with fewer than 18 vertices is traceable, and we determine all non-traceable, claw-free, 2-connected graphs with exactly 18 vertices and a...
Barker sequences and flat polynomials (2008)
Abstract. A Barker sequence is a finite sequence of integers, each ±1, whose aperiodic autocorrelations are all as small as possible. It is widely conjectured that only finitely many Barker...
Barker sequences and flat polynomials (2008)
Abstract. A Barker sequence is a finite sequence of integers, each ±1, whose aperiodic autocorrelations are all as small as possible. It is widely conjectured that only finitely many Barker...
Barker sequences and flat polynomials (2008)
Abstract. A Barker sequence is a finite sequence of integers, each ±1, whose aperiodic autocorrelations are all as small as possible. It is widely conjectured that only finitely many Barker...