Division point in the Poincaré upper half plane

AbstractWe study analytic properties function m(z, E), which is defined on the upper half-plane as an integral from the shifted L-function of an elliptic curve. We show that m(z, E) analytically continues to a meromorphic function on the whole complex plane and satisfies certain functional equation. Moreover, we give explicit formula for m(z, E) in the strip |ℑz| < 2π.

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Exact determination of gravity stresses in finite elastic slopes: Part I. Theoretical considerations

Canadian Geotechnical Journal ◽

10.1139/t83-005 ◽

1983 ◽

Vol 20 (1) ◽

pp. 47-54 ◽

Cited By ~ 10

Author(s):

V. Silvestri ◽

C. Tabib

Keyword(s):

Plane Strain ◽

Half Plane ◽

Inclination Angle ◽

Complex Variable ◽

Earth Pressure ◽

Exact Distributions ◽

Exact Determination ◽

Upper Half Plane ◽

Theoretical Considerations

The exact distributions of gravity stresses are obtained within slopes of finite height inclined at various angles, −β (β = π/2, π/3, π/4, π/6, and π/8), to the horizontal. The solutions are obtained by application of the theory of a complex variable. In homogeneous, isotropic, and linearly elastic slopes under plane strain conditions, the gravity stresses are independent of Young's modulus and are a function of (a) the coordinates, (b) the height, (c) the inclination angle, (d) Poisson's ratio or the coefficient of earth pressure at rest, and (e) the volumetric weight. Conformal applications that transform the planes of the various slopes studied onto the upper half-plane are analytically obtained. These solutions are also represented graphically.

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Revisiting the Siegel upper half plane II

Linear Algebra and its Applications ◽

10.1016/j.laa.2003.06.001 ◽

2004 ◽

Vol 376 ◽

pp. 45-67 ◽

Cited By ~ 3

Author(s):

Pedro J. Freitas ◽

Shmuel Friedland

Keyword(s):

Half Plane ◽

Upper Half Plane

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An AF Algebra Associated with the Farey Tessellation

Canadian Journal of Mathematics ◽

10.4153/cjm-2008-043-1 ◽

2008 ◽

Vol 60 (5) ◽

pp. 975-1000 ◽

Cited By ~ 11

Author(s):

Florin P. Boca

Keyword(s):

Half Plane ◽

Path Algebra ◽

Cutting Sequences ◽

Upper Half Plane ◽

Af Algebras ◽

Algebra Model

AbstractWe associate with the Farey tessellation of the upper half-plane an AF algebra encoding the “cutting sequences” that define vertical geodesics. The Effros–Shen AF algebras arise as quotients of . Using the path algebra model for AF algebras we construct, for each τ ∈ ( 0, ¼], projections (En) in such that EnEn±1En ≤ τ En.

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