Schaar's Identity

A generalization of the Gaussian sum. For p and q of opposite parity (i.e., one is even and the other is odd), Schaar's identity states


Schaar's identity can also be written so as to be valid for p, q with pq even.

See also

Gaussian Sum

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Borwein, J. M. and Borwein, P. B. Pi & the AGM: A Study in Analytic Number Theory and Computational Complexity. New York: Wiley, 1987.Evans, R. and Berndt, B. "The Determination of Gauss Sums." Bull. Amer. Math. Soc. 5, 107-129, 1981.

Referenced on Wolfram|Alpha

Schaar's Identity

Cite this as:

Weisstein, Eric W. "Schaar's Identity." From MathWorld--A Wolfram Web Resource.

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