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

单词

Kloosterman's Sum

释义

Kloosterman's Sum

(1)

where

runs through a complete set of residues Relatively Prime to

, and

is defined by

(2)

(if

and

are Relatively Prime), then

(3)

Kloosterman's sum essentially solves the problem introduced by Ramanujan

of representing sufficiently largenumbers by Quadratic Forms

. Weil improved on Kloosterman's estimate for Ramanujan's problem with the best possible estimate

(4)

(Duke 1997).

See also Gaussian Sum

References

Duke, W. ``Some Old Problems and New Results about Quadratic Forms.'' Not. Amer. Math. Soc. 44, 190-196, 1997.

Hardy, G. H. and Wright, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, p. 56, 1979.

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

Kloosterman, H. D. ``On the Representation of Numbers in the Form .'' Acta Math. 49, 407-464, 1926.

Ramanujan, S. ``On the Expression of a Number in the Form .'' Collected Papers. New York: Chelsea, 1962.

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