Quadratic Forms and Closed Geodesics
Quadratic Forms and Closed Geodesics
Quadratic Forms and Closed Geodesics
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Distribution <strong>Closed</strong> geodesics of H/Γ<br />
<strong>Quadratic</strong> <strong>Forms</strong><br />
<strong>and</strong> <strong>Closed</strong><br />
<strong>Geodesics</strong><br />
Y. Petridis<br />
<strong>Closed</strong> geodesics γ.<br />
Prime Geodesic Theorem Prime Number Theorem<br />
◮ π(x) = {γ, length (γ) ≤ ln x}<br />
π(x) ∼<br />
x<br />
◮ π(x) = {p prime, p ≤ x}<br />
ln x , x → ∞ π(x) ∼<br />
x<br />
ln x , x → ∞<br />
◮ Class number distribution (Sarnak, 1982)<br />
∑<br />
d∈D,ɛ d ≤x<br />
h(d) ∼ x 2<br />
2 ln x<br />
<strong>Quadratic</strong> <strong>Forms</strong><br />
Hyperbolic<br />
surfaces<br />
<strong>Closed</strong><br />
<strong>Geodesics</strong><br />
Spectral Theory