Abstract

We estimate sums of Kloosterman sums for a real quadratic number field F of the type where c runs through the integers of F that satisfy C⩽|N(c)|<2C, A⩽|c/c′|<B, with A<B fixed and C→∞. By x↦x′ we indicate the non-trivial automorphism of F. The Kloosterman sums are given by with .
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