KLOOSTERMAN SUMS AND A MEAN-VALUE FOR DIRICHLET POLYNOMIALS

Let a(1), a(2), a(3),... be complex numbers. Then, for epsilon > 0, M greater than or equal to 1 and T greater than or equal to 1, [GRAPHICS] where zeta(s) is Riemann's zeta-function and C-epsilon depends only on epsilon. 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). (C) 1995 Academic Press, Inc.