TY - JOUR
T1 - Nodal domains of maass forms, II
AU - Ghosh, Amit
AU - Reznikov, Andre
AU - Sarnak, Peter
PY - 2017/1/1
Y1 - 2017/1/1
N2 - In Part I we gave a polynomial growth lower-bound for the number of nodal domains of a Hecke-Maass cuspform in a compact part of the modular surface, assuming a Lindelöf hypothesis. That was a consequence of a topological argument and known subconvexity estimates, together with new sharp lower-bound restriction theorems for the Maass forms. This paper deals with the same question for general (compact or not) arithmetic surfaces which have a reflective symmetry. The topological argument is extended and representation theoretic methods are needed for the restriction theorems, together with results of Waldspurger. Various explicit examples are given and studied.
AB - In Part I we gave a polynomial growth lower-bound for the number of nodal domains of a Hecke-Maass cuspform in a compact part of the modular surface, assuming a Lindelöf hypothesis. That was a consequence of a topological argument and known subconvexity estimates, together with new sharp lower-bound restriction theorems for the Maass forms. This paper deals with the same question for general (compact or not) arithmetic surfaces which have a reflective symmetry. The topological argument is extended and representation theoretic methods are needed for the restriction theorems, together with results of Waldspurger. Various explicit examples are given and studied.
UR - http://www.scopus.com/inward/record.url?scp=85029422342&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85029422342&partnerID=8YFLogxK
U2 - 10.1353/ajm.2017.0035
DO - 10.1353/ajm.2017.0035
M3 - Article
AN - SCOPUS:85029422342
VL - 139
SP - 1395
EP - 1447
JO - American Journal of Mathematics
JF - American Journal of Mathematics
SN - 0002-9327
IS - 5
ER -