2007/08/27 by Shinji Tanimoto, Tanimoto, Shinji
Mathematics · #11A99 #FOS: Mathematics #General Mathematics (math.GM) #Number Theory (math.NT) #math.GM #math.NT #msc:11A99
paper · pdf · doi:10.48550/arxiv.0708.3521
6 pages
arxiv created 2007/08/27 · arxiv updated 2009/12/01
The arithmetic mean is the mean for addition and the geometric mean is that for multiplication. Then what kind of binary operation is associated with the arithmetic-geometric mean (AGM) due to C. F. Gauss? If it is possible to construct an arithmetic operation such that AGM is the mean for this operation, it can be regarded as an intermediate operation between addition and multiplication in view of the meaning of AGM. In this paper such an operation is introduced and several of its algebraic properties are proved.