Subconvexity Bounds for Higher-Rank Automorphic L-Functions using Spectral Reciprocity and Kuznetsov Trace Formulas

Mathematical Applications of Science Fiction We establish a new subconvexity bound for the central value of the L-function associated with a cuspidal automorphic representation of the general linear group GL(n) over the adeles of the rationals, in the level aspect, breaking the classical convexity barrier. By applying the spectral reciprocity principle derived from the higher-rank Kuznetsov trace formula, we relate the second moment of central L-values to a spectral family of automorphic forms on the unitary dual. We develop a Voronoi summation formula for GL(n) twisted by additive characters of fixed conductor, and analyze the stationary phase of the resulting hyper-Kloosterman sums. The main result provides a subconvex bound with a positive saving beyond the one-quarter exponent, conditional on the Generalized Ramanujan Conjecture for the spectral support. In addition, we obtain unconditional bounds for the case n equals three by regularizing the continuous spectrum through Eisenstein series.