“Gaussian Sum”的概念、定义、习题解题方法及翻译-数学辞典

单词

Gaussian Sum

释义

Gaussian Sum

(1)

where

and

are Relatively Prime Integers. If

, then

(2)

Gauß

showed

(3)

for Odd

. A more general result was obtained by Schaar. For

and

of opposite Parity (i.e., one is Evenand the other is Odd), Schaar's Identity states

(4)

Such sums are important in the theory of Quadratic Residues.

See also Kloosterman's Sum, Schaar's Identity, Singular Series

References

Evans, R. and Berndt, B. ``The Determination of Gauss Sums.'' Bull. Amer. Math. Soc. 5, 107-129, 1981.

Katz, N. M. Gauss Sums, Kloosterman Sums, and Monodromy Groups. Princeton, NJ: Princeton University Press, 1987.

Riesel, H. Prime Numbers and Computer Methods for Factorization, 2nd ed. Boston, MA: Birkhäuser, pp. 132-134, 1994.

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