Quadratic Forms and Closed Geodesics

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Arithmetic subgroups of SL 2 (Z) Example Fundamental Domain for Γ 0 (6) Quadratic Forms and Closed Geodesics Y. Petridis Quadratic Forms Hyperbolic surfaces Closed Geodesics Spectral Theory Hecke subgroups Γ 0 (N) az + b cz + d ∈ SL 2(Z), N|c
¡ Tesselations Quadratic Forms and Closed Geodesics Y. Petridis Quadratic Forms Hyperbolic surfaces T 1 F F TF Closed Geodesics Spectral Theory T 1 JF JF T JF T 2 UTF T 1 U 2 F T 1 UTF U 2 F UTF TU 2 F 1 0 1 1 Figure: Translates of the fundamental domain of SL 2 (Z) Figure: Triangles in the disc
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 and 20: Linear Fractional Transformations a
Page 21 and 22: Geodesics in Hyperbolic Disc Quadra
Page 23: Fundamental Domains z ∼ w ⇔ w =
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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