A theorem in multiplicative number theory

The Maximum Number of Edges in a Strongly Multiplicative Graph

Multiplicative Problems in Combinatorial Number Theory

In this thesis we look at several problems that lie in the intersection between combinatorial and multiplicative number theory. A common theme of many of these problems are estimates for and properties of the smooth numbers, those integers not divisible by any large prime factors. The first is the Ramsey-theoretic problem to determine the maximal size of a subset of the integers containing no 3...

0 - 521 - 84903 - 6 - Multiplicative Number Theory I . Classical Theory

The general rationale of analytic number theory is to derive statistical information about a sequence {an} from the analytic behaviour of an appropriate generating function, such as a power series ∑ anz or a Dirichlet series ∑ ann−s . The type of generating function employed depends on the problem being investigated. There are no rigid rules governing the kind of generating function that is app...

A multiplicative Banach-Stone theorem

The Banach-Stone theorem states that any surjective, linear mapping T between spaces of continuous functions that satisfies ‖T (f)− T (g)‖ = ‖f − g‖, where ‖ · ‖ denotes the uniform norm, is a weighted composition operator. We study a multiplicative analogue, and demonstrate that a surjective mapping T , not necessarily linear, between algebras of continuous functions with ‖T (f)T (g)‖ = ‖fg‖ m...

the maximum number of edges in a strongly multiplicative graph

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