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 pro...

The purpose of this paper is to introduce and investigate cardinal functions called pseudonet weight, weak net weight, and weak pseudonet weight. These are similar to but generally smaller than net weight. We look at how these cardinal functions relate to hereditary Lindelöf degree, hereditary density, and spread, and we study their behavior under products. An important and useful cardinal func...

where <£fc(X)=2w=i dk(ri)e^ +residue term. Hopefully, one could expand the k integral and estimate the resulting infinite series. This does not seem feasible, however, unless k{z) satisfies a certain approximate functional equation (AFE); see [5, p. 147] and [6, p. 42]. This is one reason why only k=l, k=2 are known. However, Bellman [2] has shown that, if the e~ in k(z) are replaced b...