Mass equidistribution of Hilbert modular eigenforms

Abstract

Let F be a totally real number field, and let f traverse a sequence of non-dihedral holomorphic eigencuspforms on GL(2)/F of weight (k_1,...,k_n), trivial central character and full level. We show that the mass of f equidistributes on the Hilbert modular variety as max(k_1,...,k_n) tends to infinity. Our result answers affirmatively a natural analogue of a conjecture of Rudnick and Sarnak (1994). Our proof generalizes the argument of Holowinsky-Soundararajan (2008) who established the case F = Q. The essential difficulty in doing so is to adapt Holowinsky's bounds for the Weyl periods of the equidistribution problem in terms of manageable shifted convolution sums of Fourier coefficients to the case of a number field with nontrivial unit group.

40 pages; typos corrected, nearly accepted form

References in corpus (5)

• Twisted L-functions over number fields and Hilbert's eleventh problem
• Rankin Triple Products and Quantum Chaos
• Equidistribution of cusp forms in the level aspect
• Quantum unique ergodicity for SL_2(Z)\H
• A Sieve Method for Shifted Convolution Sums

Cited by in corpus (5)

• Quantum Unique Ergodicity for half-integral weight forms
• Microlocal lifts and quantum unique ergodicity on $GL(2,{\mathbb{Q}}_p)$
• Mass equidistribution for Saito-Kurokawa lifts
• Bounds for Rankin--Selberg integrals and quantum unique ergodicity for powerful levels
• Quadratic Hecke sums and mass equidistribution