# A study of arithmetic function and visual design model

## A study of arithmetic function and visual design model

We study a theory of related arithmetic functions and develop tree model and application model of echo-system derived from arithmetic functions.

## Research

A study of arithmetic function theory has many applications in number theory. For example, using divisor function theory make a real time echo-system for animation theory. Furthermore, we develop many mathematical modeling of leaf, vein, flowers, etc. derived from arithmetic function theroy.

### Connection with Development of Institute and Division

• Since study of arithmetic function, including divisor function, is the critical source to understand number theory, it provides a boost to institute's status.
• As tree modeling using divisor functions is an application of mathematical theory to engineering, this modeling satisfies the aims of our division and institute.
• Network analysis by arithmetic functions can support the development of future technology.
• Because tree modeling can help animation and education, it help our institute's competitive power increase.

### Logical point of research subject

• Research on arithmetic functions is one of the important research subjects on number theory.
• According to MathSciNet, there are 3242 articles about divisor functions, 9759 articles for Bernoulli number, and 73 articles of composite product. Therefore, our research subject is following modern research trends in mathematics.
• Number theory research is important as a fundamental subject of mathematics.
• We are the world first team who research tree modeling using arithmetic functions.
• Adjusting Fractal theory about Riemann zeta functions, we use Fractal of Hurwitz zeta functions to create modeling for tree, leaves, and flowers.
• Developing and applying mathematical results are one of the aims of our institute.
• Since tree modeling using arithmetic functions can count the number of leaves and branches of trees, our research can support not only biology about the growth of trees, but computer graphics including game, animation, virtual reality.

## Expected effect

Divisor tree model gives us an animation model for environment of online game. Since tree modeling using arithmetic functions can count the number of leaves and branches of trees, our research can support not only biology about the growth of trees, but computer graphics including game, animation, virtual reality. If we can apply tree modeling using divisor functions to video games, we can create enough leaves as fast as we want. Therefore, we can save time and electronic resources by eliminating extra trees and branches.

Division of Mathematical Models Kim, Daeyeoul
Tel. +82-42-717-5748