Quadratic Forms and Closed Geodesics

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The Hyperbolic Disc Quadratic Forms and Closed Geodesics Y. Petridis Quadratic Forms ◮ Model of hyperbolic geometry H = {z = x + iy, |z| < 1} Hyperbolic surfaces Closed Geodesics Spectral Theory ◮ Hyperbolic metric ds 2 = dx 2 + dy 2 (1 − (x 2 + y 2 )) 2 d(0, z) = ln 1 + |z| 1 − |z| ,
Geodesics in Hyperbolic Disc Quadratic Forms and Closed Geodesics Y. Petridis Quadratic Forms Hyperbolic surfaces Closed Geodesics Spectral Theory ◮ Semicircles perpendicular to boundary ◮ Diameters
Page 1 and 2: Quadratic Forms and Closed Geodesic
Page 3 and 4: Pell’s Equation Quadratic Forms a
Page 9 and 10: Indefinite Quadratic Forms ◮ Q(x,
Page 15 and 16: Class Numbers h(d) = number of ineq
Page 17 and 18: From Quadratic Forms to Hyperbolic
Page 19: Linear Fractional Transformations a
Page 23 and 24: Fundamental Domains z ∼ w ⇔ w =
Page 25 and 26: ¡ Tesselations Quadratic Forms and
Page 27 and 28: Pell’s Equation and Lengths of Cl
Page 29 and 30: Distribution Closed geodesics of H/
Page 31: The Laplace Operator Quadratic Form
Page 34 and 35: Contour plots of eigenfunctions of
Page 36 and 37: The Riemann Hypothesis ◮ Think of
Page 38 and 39: Relations of RH with spectral theor
Page 40 and 41: Duality between periods and eigenva
Page 42 and 43: Simple trace formula Quadratic Form

Quadratic Forms and Closed Geodesics

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