The variance of arithmetic measures associated to closed geodesics on the modular surface

Wenzhi Luo, Zeév Rudnick, Peter Sarnak

Type: Article

Publication Date: 2009-01-01

Citations: 11

DOI: https://doi.org/10.3934/jmd.2009.3.271

Abstract

We determine the variance for the fluctuations of the arithmetic measuresobtained by collecting all closed geodesics on the modular surface with thesame discriminant and ordering them by the latter. This arithmetic variancediffers by subtle factors from the variance that one gets when consideringindividual closed geodesics when ordered by their length. The arithmeticvariance is the same one that appears in the fluctuations of measuresassociated with quantum states on the modular surface.

Locations

Journal of Modern Dynamics - View
arXiv (Cornell University) - View - PDF
Journal of Modern Dynamics - View
arXiv (Cornell University) - View - PDF
Journal of Modern Dynamics - View
arXiv (Cornell University) - View - PDF

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Works Cited by This (40)

Action	Title	Year	Authors
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+	Topics in Classical Automorphic Forms	1997	Henryk Iwaniec
+	Lectures on Modular Functions of One Complex Variable	1983	Hans Maaß
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+ PDF	Sur certains groupes d'opérateurs unitaires	1964	André Weil
+	Hyperbolic distribution problems and half-integral weight Maass forms	1988	William Duke
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+	Heegner points, cycles and Maass forms	1993	Svetlana Katok Peter Sarnak