Some corrections for Bourgain-Gamburd-Sarnak’s paper “Generalizations of Selberg’s 3/16 theorem and affine sieve”

I am currently reading the paper

J. Bourgain, A. Gamburd, P. Sarnak, Generalizations of Selberg’s \frac{3}{16} theorem and affine sieve, Acta Mathematica, 207 (2011), 255-290

and I noticed some problems with Section 3. Namely, there are two errors. The line “taking z = w = i in (3.2)” is plainly wrong; since that would yield u(i,i) = 0 which is not desired. Further, equation (3.3) is wrong as stated; it should be \displaystyle \lVert g \rVert^2 = 4 \frac{u(gi,i)}{\det(g)} + 2.


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