5 citations · 8 across the 7 of their papers we have counts for
7 papers · 1 filter
A classification of -linear maps from to
Charles L. Samuels
A 2009 article of Allcock and Vaaler explored the -vector space , showing how to…
Lower bounds on the projective heights of algebraic points
Charles L. Samuels
If are algebraic numbers such that for some integer , then a theorem of Beukers and Zagier gives the best possibl…
Two inequalities on the areal Mahler measure
Stephen K. K. Choi, Charles L. Samuels
Recent work of Pritsker defines and studies an areal version of the Mahler measure. We further explore this function with a particular focus on the case where its value is small, a…
A collection of metric Mahler measures
Charles L. Samuels
Let denote the Mahler measure of the algebraic number . In a recent paper, Dubickas and Smyth constructed a metric version of the Mahler measure on the multiplicative gro…
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…
Estimating heights using auxiliary functions
Charles L. Samuels
Several recent papers construct auxiliary polynomials to bound the Weil height of certain classes of algebraic numbers from below. Following these techniques, the author gave a gen…