Approximation of the Multiplication Table Function

Details Approximation of the Multiplication Table Function Approximation of the Multiplication Table Function

2006-03-28

arxiv.org/abs/math/0603644v2

Mathematics

Number Theory

5 pages

Scientific paper

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

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