Functorial products for GL2×GL3 and functorial symmetric cube for GL2

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On the complex moments of symmetric power $L$-functions at $s = 1$ (2004, methodology): “Hypothesis Sym(f) is known unconditionally for k up to 4: it is tautological if k = 1 and follows from the work of Gelbart/Jacquet for k = 2 and from the more recent works of Kim/Shahidi and Kim when k = 3, 4 [5, 15, 16, 14].”
Generalised form of a conjecture of Jacquet and a local consequence (2006, methodology): “is that the local factors of L3(s,Π) have no poles at s = 1 2 . This is clearly true for the local factors given in terms of representations of the Weil-Deligne group by the Kim-Shahidi estimate from [11] used above. For the local factors given by Shahidi in [22] it is also true, we check this for t”
Sieving for mass equidistribution (2008, methodology): “s/ > 1 is known for m 6 8 by the works of [KS00] and [Kim03].”
Rankin Triple Products and Quantum Chaos (2008, methodology): “[2] J. Cogdell, I. Piatetski-Shapiro, A converse theorem for GL4, Math.”
A density theorem on automorphic L-functions and some applications (2005, unknown): “For m = 1, 2, 3, 4, it is known (see [7] for m = 1, [2] for m = 2 and [9, 10, 11] for m = 3, 4) that the function (1.”
Local L-Functions for Split Spinor Groups (2002, unknown): “[11], [12]).”