Quadratic Forms and Closed Geodesics
Quadratic Forms and Closed Geodesics
Quadratic Forms and Closed Geodesics
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Pell’s Equation <strong>and</strong> Lengths of <strong>Closed</strong><br />
<strong>Geodesics</strong><br />
<strong>Quadratic</strong> <strong>Forms</strong><br />
<strong>and</strong> <strong>Closed</strong><br />
<strong>Geodesics</strong><br />
Y. Petridis<br />
<strong>Quadratic</strong> <strong>Forms</strong><br />
Hyperbolic<br />
surfaces<br />
N(g)<br />
1<br />
∫ N(g)<br />
1<br />
1<br />
y dy = ln N(g) = ln(ɛ2 d )<br />
<strong>Closed</strong><br />
<strong>Geodesics</strong><br />
Spectral Theory<br />
x<br />
1<br />
N(g)<br />
Theorem<br />
The lengths of the closed geodesics for the hyperbolic<br />
surface H/SL 2 (Z) are 2 log ɛ d with multiplicity h(d),<br />
d ∈ D.