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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: $$ \mathfrak{N}(n)=n^{\frac{\log 2}{\log\log n}(1+\frac{387}{200\log\log n})}. $$