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Fields of Rationality of Cusp Forms | | John Binder
; | | Date: |
3 Feb 2015 | | Abstract: | In this paper, we prove that for any totally real field $F$, weight $k$, and
nebentypus character $chi$, the proportion of Hilbert cusp forms over $F$ of
weight $k$ and character $chi$ with bounded field of rationality approaches
zero as the level grows large. This answers, in the affirmative, a question of
Serre. The key intermediate result, which we believe is interesting in its own
right, is a Plancherel equidsitribution theorem for cusp forms with fixed
central character, whose proof builds on earlier work of Shin and Shin-Templier
by introducing a bound for certain families of orbital integrals. | | Source: | arXiv, 1502.0976 | | Services: | Forum | Review | PDF | Favorites | |
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