12 citations · 16 across the 10 of their papers we have counts for
7 papers · 1 filter
Polynomials whose reducibility is related to the Goldbach conjecture
Peter B. Borwein, Stephen K. K. Choi, Greg Martin +1
We introduce a collection of polynomials , associated to each positive integer , whose divisibility properties yield a reformulation of the Goldbach conjecture. While this…
The multivariate integer Chebyshev problem
P. B. Borwein, I. E. Pritsker
The multivariate integer Chebyshev problem is to find polynomials with integer coefficients that minimize the supremum norm over a compact set in $\C^d.$ We study this problem on g…
A note on Barker polynomials
Peter Borwein, Tamas Erdelyi
We give a new proof of the fact that Barker polynomials of even degree greater than 12, and hence Barker sequences of odd length greater than 13 do not exist. This is intimately ti…
Sign Changes of the Liouville function on quadratics
Peter Borwein, Stephen K. K. Choi, Himadri Ganguli
Let denote the Liouville function. Complementary to the prime number theorem, Chowla conjectured that \vspace{1mm} \noindent {\bf Conjecture (Chowla).} {\em \begin{equation}…
Completely multiplicative functions taking values in
Peter Borwein, Stephen K. K. Choi, Michael Coons
Define {\em the Liouville function for }, a subset of the primes , by where is the number of prime factors of coming from counting…
Transcendence of the Gaussian Liouville number and relatives
Peter Borwein, Michael Coons
{\em The Liouville number}, denoted , is defined by where the th bit is given by ${1/2}(1+\gl(n))$; here $\gl$ is the Liouville function fo…
Transcendence of Power Series for Some Number Theoretic Functions
Michael Coons, Peter Borwein
We give a new proof of Fatou's theorem: {\em if an algebraic function has a power series expansion with bounded integer coefficients, then it must be a rational function.} This res…