“Ramanujan's Sum”的概念、定义、习题解题方法及翻译-数学辞典

单词

Ramanujan's Sum

释义

Ramanujan's Sum

The sum

(1)

where

runs through the residues Relatively Prime to

, which is important in the representation of numbers by thesums of squares. If

(i.e.,

and

' are Relatively Prime), then

(2)

For argument 1,

(3)

where

is the Möbius Function, and for general

(4)

See also Möbius Function, Weyl's Criterion

References

Vardi, I. Computational Recreations in Mathematica. Redwood City, CA: Addison-Wesley, p. 254, 1991.

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