  We prove asymptotics for real moments of the logarithmic derivative of
characteristic polynomials evaluated at $1-\frac{a}{N}$ in unitary, even
orthogonal, and symplectic ensembles, where $a>0$ and $a=o(1)$ as the size $N$
of the matrix goes to infinity. Previously, such asymptotics were known only
for integer moments (in the unitary ensemble by the work of Bailey, Bettin,
Blower, Conrey, Prokhorov, Rubinstein and Snaith, and in orthogonal and
symplectic ensembles by the work of Alvarez and Snaith), except that in the odd
orthogonal ensemble real moments asymptotics were obtained by Alvarez,
Bousseyroux and Snaith. Our proof is new and does not make use of the
aforementioned integer moments results, and is different from the method in the
work of Alvarez et al for the odd orthogonal ensemble.
