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Award ID contains: 1946333

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  1. (, Compositio Mathematica)
    null (Ed.)
    Let $$E/\mathbb {Q}$$ be a number field of degree $$n$$ . We show that if $$\operatorname {Reg}(E)\ll _n |\!\operatorname{Disc}(E)|^{1/4}$$ then the fraction of class group characters for which the Hecke $$L$$ -function does not vanish at the central point is $$\gg _{n,\varepsilon } |\!\operatorname{Disc}(E)|^{-1/4-\varepsilon }$$ . The proof is an interplay between almost equidistribution of Eisenstein periods over the toral packet in $$\mathbf {PGL}_n(\mathbb {Z})\backslash \mathbf {PGL}_n(\mathbb {R})$$ associated to the maximal order of $$E$$ , and the escape of mass of the torus orbit associated to the trivial ideal class. 
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