# Approximation of the Multiplication Table Function

Research paper by Mehdi Hassani

Indexed on: 02 May '06Published on: 02 May '06Published in: Mathematics - Number Theory

#### Abstract

In this paper, considering the concept of Universal Multiplication Table, we show that for every $n\geq 2$, the inequality: $$M(n)=#\{ij|1\leq i,j\leq n\}\geq\frac{n^2}{\mathfrak{N}(n^2)},$$ holds true with: $$\mathfrak{N}(n)=n^{\frac{\log 2}{\log\log n}(1+\frac{387}{200\log\log n})}.$$