Mass equidistribution for automorphic forms of cohomological type on 𝐺𝐿₂

Marshall, Simon ¹

¹ School of Mathematics, The Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540

Journal of the American Mathematical Society, Tome 24 (2011) no. 4, pp. 1051-1103

Résumé

We extend Holowinsky and Soundararajan’s proof of quantum unique ergodicity for holomorphic Hecke modular forms on $SL(2,\mathbb {Z})$, by establishing it for automorphic forms of cohomological type on $GL_2$ over an arbitrary number field which satisfy the Ramanujan bounds. In particular, we have unconditional theorems over totally real and imaginary quadratic fields. In the totally real case we show that our result implies the equidistribution of the zero divisors of holomorphic Hecke modular forms, generalising a result of Rudnick over $\mathbb {Q}$.

Détail

DOI : 10.1090/S0894-0347-2011-00700-5

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