Quantum Unique Ergodicity of Degenerate Eisenstein Series on GL(n)

Content Provider	Semantic Scholar
Author	Zhang, Liyang
Copyright Year	2016
Abstract	In the area of quantum chaos, it is of great interest to study the distribution of the $$L^2$$L2-mass of eigenfunctions of the Laplacian as eigenvalues tend to infinity. Luo and Sarnak first formulated and proved arithmetic quantum unique ergodicity for the continuous spectrum (spanned by Eisenstein series) of the hyperbolic Laplacian on $$SL(2,\mathbb {Z})\backslash \mathbb {H}$$SL(2,Z)\H by utilizing the sub-convexity bounds of L-functions associated to Maass cusp forms. In this paper, we build on Luo and Sarnak’s method and explore the structure properties of the constant terms of GL(n) Eisenstein series and extend their results to higher ranks. We prove quantum unique ergodicity for a subspace of the continuous spectrum spanned by the degenerate Eisenstein Series on GL(n).
Starting Page	1
Ending Page	48
Page Count	48
File Format	PDF HTM / HTML
DOI	10.1007/s00220-019-03464-x
Alternate Webpage(s)	http://export.arxiv.org/pdf/1609.01386
Alternate Webpage(s)	https://arxiv.org/pdf/1609.01386v1.pdf
Alternate Webpage(s)	https://doi.org/10.1007/s00220-019-03464-x
Volume Number	369
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article