Subconvexity Bounds for L-functions of Maass Forms via the Spectral Large Sieve-VERSÃO 3

This monograph establishes a subconvexity bound for the L-functions associated with Hecke-Maass cusp forms for the full modular group SL(2, Z) in the spectral aspect. Let uj be a Hecke-Maass cusp form with spectral parameter tj and normalized Fourier coefficients j(n). The convexity bound for the associated L-function L(s, uj) on the critical line Re(s)=1/2 is O(tj1/2+). By employing the spectral large sieve inequalities of Deshouillers and Iwaniec, combined with the amplification method, we derive a bound of the form L(1/2+it, uj) tj1/2 - + for some > 0. The proof necessitates a rigorous treatment of the Kuznetsov trace formula, the estimation of off-diagonal terms via Kloosterman sums, and the analytic properties of the spectral resolution of the Laplacian on the modular surface.