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Squares in Polynomial Product Sequences
Squarefull numbers Polynomial Product Sequences Number Theory
2011/8/31
Abstract: Let F(n) be a polynomial of degree at least 2 with integer coefficients. We consider the products N_x=\prod_{1 \le n \le x} F(n) and show that N_x should only rarely be a perfect power. In p...
Ehrhart's polynomial for equilateral triangles in $\mathbb Z^3$
Ehrhart polynomial linear Diophantine equations lattice points equilateral triangles sequences regular integral polytopes
2011/8/25
Abstract: In this paper we calculate the Ehrhart's polynomial associated with a 2-dimensional regular polytope (i.e. equilateral triangles) in $\mathbb Z^3$. The polynomial takes a relatively simple f...
From logarithmic to subdiffusive polynomial fluctuations for internal DLA and related growth models
internal diffusion limited aggregation cluster growth
2010/12/6
We consider a family of cluster growth models on Zd, which generalize internal diffusion limited aggregation (internal DLA). The latter model is simplest to describe:random walks start at the origin, ...
Polynomial estimates, exponential curves and Diophantine approximation
Polynomial estimates exponential curves Diophantine approximation
2010/12/10
Let ∈ (0, 1) \ Q and K = {(ez, e z) : |z| ≤ 1} ⊂ C2. If P is a polynomial of degree n in C2, normalized by kPkK = 1, we obtain sharp estimates for kPk2 in terms of n, where 2 is the closed u...