The hyperbolic lattice point problem in conjugacy classes
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AbstractFor Γ a cocompact or cofinite Fuchsian group, we study the hyperbolic lattice point problem in conjugacy classes, which is a modification of the classical hyperbolic lattice point problem. We use large sieve inequalities for the Riemann surfaces ${{\Gamma\backslash{\mathbb{H}}}}$ to obtain average results for the error term, which are conjecturally optimal. We give a new proof of the error bound ${O(X^{2/3})}$, due to Good. For ${{\mathrm{SL}_{2}({\mathbb{Z}})}}$ we interpret our results in terms of indefinite quadratic forms.
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2016 ◽
Vol 145
(4)
◽
pp. 1421-1437
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1969 ◽
Vol 1
(4)
◽
pp. 534-555
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