On sums of hyper-Kloosterman sums
On sums of hyper-Kloosterman sums
Abstract A formula of Kuznetsov allows one to interpret a smooth sum of Kloosterman sums as a sum over the spectrum of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>GL</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mn>2</m:mn> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> {\operatorname{GL}(2)} automorphic forms. In this paper, we construct a similar formula for the first …