Spectral Theory of Infinite-Area Hyperbolic Surfaces
David Borthwick
Progress in Mathematics, Vol. 256
Birkhauser Boston, 2007
Birkhauser Boston, 2007
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| Chapter 9 notes |
The statement on p. 169 that the
O(r^n) bound was proven in Cuevas-Vodev [47] is incorrect. They
establish the bound for a sector excluding the negative real axis [47,
Prop. 1.2], but their proof of [47, Prop. 1.3], which extends the
result to the whole plane, is incorrect. I have given a corrected
version of this argument in [Borthwick, Upper and lower bounds on resonances for manifolds hyperbolic near infinity, Comm. PDE 33 (2008), 1507--1539.]. |
| Theorem
11.3 |
The extra n_c/4 appearing in
(11.12) may seem a little odd. To verify that it is correct, we
can compare to the Selberg trace formula in the case of finite
area. A copy of that argument is available here. It is not clear to me why
this term is absent in Guillopé-Zworski [87, Thm. 5.7], but my
guess is that the modified Hilbert space for the cusp ends affects the
definition of the 0-trace. |