On Effective Upper Bound for Huber’s Constant

We determine an effective upper bound for Huber’s constant in the prime geodesic theorem on cofinite Fuchsian groups in the previously uncovered case of orbifolds on which the length of the shortest prime geodesic does not exceed 4/3. Huber’s constant is relevant for obtaining effective, numerically computable, bounds for various analytic quantities which appear in the Arakelov theory of algebraic curves. The result is illustrated by finding an upper bound for this constant on (2, 3, 7) triangle group. We also calculate an effective upper bound for Faltings’s delta function on the Klein quartic.