Establishes strong hybrid subconvexity bounds for twisted selfdual GL3 L-functions via a new GL3 x GL2 to GL4 x GL1 spectral reciprocity formula together with an averaged Lindelof bound on Dirichlet L-functions.
Young, ``The Second Moment of the GL_3 Standard L -Function on the Critical Line'' https://arxiv.org/abs/2407.06962v1, preprint (2024), 32 pages
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A nontrivial bound is proved for the average shifted convolution sum B(H,N) of Fourier coefficients of Hecke-Maass cusp forms on GL(d1) x GL(d2) for H at least N^{1-4/(d1+d2)+eps}.
For self-dual GL(3) Hecke-Maass cusp forms, the normalized sum x^{-1/3} Δ_f(x) has a distribution function with quantitative convergence rate.
A new lower bound m(σ) ≥ 17/(26-28σ) holds for the supremum of m such that the m-th moment integral of |L(σ+it, sym²f)| grows at most like T^{1+ε} when 5/8 ≤ σ ≤ 52/73.
Assuming the generalized Ramanujan conjecture, ∫_T^{2T} |L(1/2+it, π)|^2 dt ≪_π T^{d/2} / log^{η_d} T holds for small η_d > 0 when d ≥ 3.
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Average shifted convolution sum for $GL(d_1)\times GL(d_2)$
A nontrivial bound is proved for the average shifted convolution sum B(H,N) of Fourier coefficients of Hecke-Maass cusp forms on GL(d1) x GL(d2) for H at least N^{1-4/(d1+d2)+eps}.