This research manuscript establishes the Apex Dominance Criterion for the rank-3 symplectic similitude group GSp6, providing a rigorous proof of the first unconditional subconvexity bound for the associated degree-8 spin L-function. The analysis utilizes a multi-dimensional Duke-Friedlander-Iwaniec delta-method integrated into the spectral decomposition of the Kuznetsov trace formula. This framework reduces the analytic estimation of the L-function at the critical point (1/2 + it) to the evaluation of shifted convolution sums of triple-product coefficients. The core technical contribution is the derivation of a C3-type Voronoi summation formula associated with the long element of the Weyl group for GSp6. By estimating the resulting hyper-Kloosterman sums—constrained by the Riemann Hypothesis for varieties over finite fields (Deligne, 1974) —the paper proves a power-saving of X^ (1 - 15/128). This saving is anchored in the Kim-Sarnak refined estimates (theta <= 7/64) for the constituent GL2 representations. The resulting subconvexity bound serves as an analytic proof of the non-vanishing of the central L-value and the stationarity of the underlying trilinear automorphic period. This work provides the necessary mathematical closure for identifying stationary invariants in higher-rank symplectic groups and serves as a formal registry for the adelic architecture of triple product transfers.
Andrew Kim (Tue,) studied this question.