Kloosterman Sums and a Mean Value for Dirichlet Polynomials

Abstract

Let a 1, a 2, a 3,... be complex numbers. Then, for ϵ > 0, M ≥ 1 and T ≥ 1, [formula] where ζ( s) is Riemann′s zeta-function and C ϵ depends only on ϵ. The proof is based on a technical refinement within the circle of ideas to be found in Deshouillers and Iwaniec′s paper: Kloosterman sums and Fourier coefficients of cusp forms ( Invent. Math. 70 (1982), 219-288).