Nodal Domains of Maass Forms I
نویسندگان
چکیده
This paper deals with some questions that have received a lot of attention since they were raised by Hejhal and Rackner in their 1992 numerical computations of Maass forms. We establish sharp upper and lower bounds for the L2-restrictions of these forms to certain curves on the modular surface. These results, together with the Lindelof Hypothesis and known subconvex L∞-bounds are applied to prove that locally the number of nodal domains of such a form goes to infinity with its eigenvalue.
منابع مشابه
Lectures on Maass Forms Postech , March 25 - 27 , 2007
will be treated; the general theory for congruence subgroups Γ0(N) is similar in philosophy but more involved in details. For detailed treatment of Maass forms in book form, the reader is referred to e.g. Borel [2], Bump [3], Iwaniec [4], and Ye [20]. Even for the simplest case (1.1), there are already big amount of materials in the literature. To explain these materials in such a short time, I...
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