Analytic twists of GL2×GL2$\rm GL_2\times \rm GL_2$ automorphic forms

Abstract

AbstractLet f and g be holomorphic or Maass cusp forms for with normalized Fourier coefficients and , respectively. In this paper, we prove nontrivial estimates for the sum where , , is a large parameter and is some nonlinear real‐valued smooth function. Applications of these estimates include a subconvex bound for the Rankin–Selberg L‐function in the t‐aspect, an improved estimate for a nonlinear exponential twisted sum and the following asymptotic formula for the sum of the Fourier coefficients of certain Eisenstein series for any .