Arithmetic Quantum Chaos

By Jens Marklof. 2006

196 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1df92d7190e42a2d231cc431b578d70d0d0c916a

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In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

ON THE ASYMPTOTIC DISTRIBUTION OF ZEROS OF MODULAR FORMS (2005, background): “1 ,ittranspiresthat,again,one hasto beat the\convexity bound" on thecentralvalue,forwhich oneusesGRH.”
Automorphic distributions, L-functions, and Voronoi summation for GL(3) (2004, background): “19) would imply the Lindelöf Conjecture: |ζ(1/2 + it)| = O(1 + |t|ε), for any ε > 0 [33].”
ENTROPY AND THE LOCALIZATION OF EIGENFUNCTIONS. (2008, background): “At the quantum level, one expects that the chaotic features should express themselves in certain behaviours of the eigenfunctions of the Laplacian, or in the distribution of its eigenvalues (see [Sa95]).”
Quantum unique ergodicity for SL_2(Z)\H (2009, background): “For more complete accounts of the quantum unique ergodicity problem the reader may consult [7], [9], [11], [13] and references therein; a comprehensive introduction to the theory of Maass forms is provided in [4].”
Mass equidistribution for Hecke eigenforms (2008, background): “For illuminating accounts on this conjecture we refer the reader to [6], [7], [8], [9], [10], [12], [14], [13], [18].”
Geometric control in the presence of a black box (2004, result): “Apart from the beautifull, more p cise but particular results on arithmetic surfaces [34],[31], this result seems to be the first one show ing that there exist some invariant measures which arenot the semi-classical measures of any sequence of eigenfuncti ons.”
Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds (2005, background): “[16] P. Sarnak.”