Finite transformation formulae involving the Legendre symbol
Kenneth S. Williams · Pacific Journal of Mathematics · 1970
Let p denote an odd prime. The following three identities (transformation formulae) involving the Legendre symbol ί — j are known to be valid for any complex-valued function F de-fined on the integers, which is periodic with period p: Σ F(x) + Σ (~V(χ) = Σ *W> x=0 x = 0 \\ P / x = 0 v — i p—i //y.2 An \\ P —i / n \\ Σ F(x) + Σ 1^—^)F(X) = Σ ^ ( * +- I a