Infinitely often dense bases and geometric structure of sumsets.

Item

Title: Infinitely often dense bases and geometric structure of sumsets.
Identifier: AAI3213245
identifier: 3213245
Creator: Lee, Jaewoo.
Contributor: Adviser: Melvyn B. Nathanson
Date: 2006
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: We'll discuss two problems related to sumsets.;Nathanson constructed bases of integers with prescribed representation functions, then asked how dense bases for integers can be in such cases. Let A(-x, x) be the number of elements of A whose absolute value is less than or equal to x, then it's easy to see that A(-x, x) << x1/2 if its representation function is bounded, giving us a general upper bound. Chen constructed unique representation bases for integers with A(-x, x) ≥ x1/2-epsilon infinitely often. In the first chapter, we'll construct bases for integers with a prescribed representation function with A(-x, x) > x1/2/&phis;(x) infinitely often where &phis;(x) is any nonnegative real-valued function which tends to infinity.;In the second chapter, we'll see how sumsets appear geometrically. Assume A is a finite set of lattice points and h*D=h&dot;x:x∈conv A is a full dimensional polytope. Then we'll see that there is a constant rho with the following property: for any positive integer h, any integral point in the polytope h * Delta, whose distance to the boundary is bigger than rho, belongs to the sumset hA..
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.

Item sets: CUNY Legacy ETDs

Media: Infinitely often dense bases and geometric structure of sumsets.