Document Type
Lecture
Publication Date
9-6-2019
Abstract
A subset H of non-negative integers is called an essential component if d(A + H) > d(A) for all A ⊆ ℕ with 0 < d(A) < 1, where d(A) is the lower asymptotic density of A. How sparse can an essential component be? The best-known result of this problem is due to Ruzsa. Here, we generalize the problem to the additive group (��ₚ[t], +). Our result is analogous to but more precise than Ruzsa's result in the integers. We also construct an explicit example of an essential component in ��ₚ[t] with a small counting function, based on an argument of Wirsing. This is joint work with Thái Hoàng Lê.
Relational Format
presentation
Recommended Citation
Ge, Zhenchao, "Essential Components in ��ₚ[t]" (2019). Algebra/Number Theory Seminar. 25.
https://egrove.olemiss.edu/math_algebra_number_theory/25
