A novel operation associated with Gauss' arithmetic-geometric means

Details A novel operation associated with Gauss' arithmetic-geometric means A novel operation associated with Gauss' arithmetic-geometric means

2007-08-27

arxiv.org/abs/0708.3521v1

Mathematics

Number Theory

6 pages

Scientific paper

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.

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