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Journal für die reine und angewandte Mathematik

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The distribution of values of the Poincaré pairing for hyperbolic Riemann surfaces

Yiannis N. Petridis1 / Morten S. Risager2

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Citation Information: Journal für die reine und angewandte Mathematik. Volume 2005, Issue 579, Pages 159–173, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/crll.2005.2005.579.159, July 2005

Publication History

Received:
19. Januar 2004
Published Online:
2005-07-27

Abstract

For a cocompact group of SL2(ℝ) we fix a non-zero harmonic 1-form α. We normalize and order the values of the Poincaré pairing 〈 γ,α〉 according to the length of the corresponding closed geodesic l(γ). We prove that these normalized values have a Gaussian distribution.

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[1]
C. J. Mozzochi
Israel Journal of Mathematics, 2013, Volume 195, Number 1, Page 71
[2]
Yiannis N. Petridis and Morten S. Risager
Forum Mathematicum, 2008, Volume 20, Number 5

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