4 papers
Almost Alternating Sums
Kevin O'Bryant, Bruce Reznick, Monika Serbinowska
Writing for a general mathematical audience, we provide elementary upper and lower bounds on the growth (as a function of N) of the sum \sum_{n=1}^N (-1)^{\floor{n x}} for various…
On the absence of uniform denominators in Hilbert's 17th problem
Bruce Reznick
Hilbert showed that for most there exist psd forms of degree which cannot be written as a sum of squares of forms. His 17th problem asked whether, in t…
Patterns of dependence among powers of polynomials
Bruce Reznick
Let F = {f_1,...,f_r} be a family of polynomials and let the ticket of F, T(F), denote the set of integers m so that is linearly dependent. We show that |T(F)| \le (r-1)(…
Lattice polytopes with distinct pair-sums
M. D. Choi, T. Y. Lam, Bruce Reznick
Let P be a lattice polytope in R^n, and let P \cap Z^n = {v_1,...,v_N}. If the N + \binom N2 points 2v_1,...,2v_N; v_1+v_2,...v_{N-1}+v_N are distinct, we say that P is a "distinct…