Abstract
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.
Original language | English |
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Pages (from-to) | 1395-1447 |
Number of pages | 53 |
Journal | American Journal of Mathematics |
Volume | 139 |
Issue number | 5 |
DOIs | |
State | Published - 2017 |
Bibliographical note
Publisher Copyright:© 2017 by Johns Hopkins University Press.
Funding
Manuscript received January 3, 2016; revised July 17, 2017. Research of the first author supported in part by IAS, the College of A&S and the Department of Mathematics of his home university, and the Simons Foundation for a Collaboration Grant; research of the second author supported in part by the Veblen Fund at IAS, the ERC grant 291612 and by the ISF grant 533/14; research of the second and third authors supported in part by a BSF grant; research of the third author supported by NSF grant 1302952. American Journal of Mathematics 139 (2017), 1395–1447. ©c 2017 by Johns Hopkins University Press.
Funders | Funder number |
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National Science Foundation | 1302952 |
Simons Foundation | |
Bloom's Syndrome Foundation | |
Iowa Academy of Science | |
Iowa Science Foundation | 533/14 |
European Commission | 291612 |