On the statistics of the minimal solution of a linear Diophantine equation and uniform distribution of the real part of orbits in hyperbolic spaces

Risager, Morten S.; Rudnick, Zeév

doi:10.1090/conm/484/09475

Cited by 14 publications

(20 citation statements)

References 9 publications

(14 reference statements)

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“…The volume of S M,ξ can be evaluated in closed form using the substitution z = tan t: 20) where B M (ξ, t) is the area of the region (r cos θ, r sin θ) ∈ [0, 1] 2 :…”

Section: Pair Correlation Of {φ(γ)}mentioning

confidence: 99%

Pair correlation of angles between reciprocal geodesics on the modular surface

Boca

Paşol

Popa

et al. 2014

Algebra Number Theory

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The existence of the limiting pair correlation for angles between reciprocal geodesics on the modular surface is established. An explicit formula is provided, which captures geometric information about the length of reciprocal geodesics, as well as arithmetic information about the associated reciprocal classes of binary quadratic forms. One striking feature is the absence of a gap beyond zero in the limiting distribution, contrasting with the analog Euclidean situation.

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“…The volume of S M,ξ can be evaluated in closed form using the substitution z = tan t: 20) where B M (ξ, t) is the area of the region (r cos θ, r sin θ) ∈ [0, 1] 2 :…”

Section: Pair Correlation Of {φ(γ)}mentioning

confidence: 99%

Pair correlation of angles between reciprocal geodesics on the modular surface

Boca

Paşol

Popa

et al. 2014

Algebra Number Theory

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“…In this case, the directions correspond to the projections of the orbit Γw onto a closed horosphere in Γ ∞ \H n . The uniform distribution of the projected orbit was proved by Good [7,14] (see also Rudnick and Risager [12] for an interesting number-theoretic application). We will show that local statistics have the same limit distribution as in the non-cuspidal case.…”

Section: Introductionmentioning

confidence: 95%

Directions in hyperbolic lattices

Marklof

Vinogradov

2015

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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Translation of the Bible or any other text unavoidably involves a determination about its meaning. There have been different views of meaning from ancient times up to the present, and a particularly Enlightenment and Modernist view is that the meaning of a text amounts to whatever the original author of the text intended it to be. This article analyzes the authorial-intent view of meaning in comparison with other models of literary and legal interpretation. Texts are anchors to interpretation but are subject to individualized interpretations. It is texts that are translated, not intentions. The challenge to the translator is to negotiate the meaning of a text and try to choose the most salient and appropriate interpretation as a basis for bringing the text to a new audience through translation.

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“…We consider the angles between geodesic rays (ω → γω) in the upper half plane H, connecting a fixed point ω ∈ H with the (finitely many) points γω in its Γ-orbit, lying in increasingly large hyperbolic balls. These angles are wellknown to be uniformly distributed (see, e.g., [19]) and their uniform distribution in angular sectors can be made effective [1,7,8,14,15,16,20,21].…”

Section: Introductionmentioning

confidence: 99%