Notes on the Generalized Ramanujan Conjectures

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Prime and almost prime integral points on principal homogeneous spaces (2009, methodology): “This allows us to make use of the well-developed analytic methods [DRS], [GN1] for counting points in such orbits in a big Euclidean ball, as well as the strong bounds towards the general Ramanujan conjectures that are known from the theory of automorphic forms (see [Cl1] and [ S1 ]).”
On the Voronoĭ formula for GL(n) (2013, background): “Recent applications of the formula for GL ( 3 ) may be found in Miller-Schmid [28, 30], Sarnak-Watson [32] and Li [26, 27].”
Generalization of Selberg’s $$ \frac{3}{{16}} $$ theorem and affine sieve (2011, background): “See [29] for the sharpest known bounds towards Selberg’s 1 4 Conjecture as well as bounds towards the Ramanujan Conjectures for more general groups.”
Generalization of Selberg's 3/16 Theorem and Affine Sieve (2009, background): “See [29] for the sharpest known bounds towards Selberg’s 1 4 Conjecture as well as bounds towards the Ramanujan Conjectures for more general groups.”
Affine linear sieve, expanders, and sum-product (2010, background): “Progress on the general Ramanujan conjectures for G(Q)\G(A) (see [15, 51, 57]) establish Conjecture 1.”