Effective bounds for Huber’s constant and Faltings’s delta function

Avdispahić, Muharem

doi:10.1090/mcom/3631

Effective bounds for Huber’s constant and Faltings’s delta function
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Math. Comp. 90 (2021), 2381-2414 Request permission

Abstract:

By a closer inspection of the Friedman-Jorgenson-Kramer algorithm related to the prime geodesic theorem on cofinite Fuchsian groups of the first kind, we refine the constants therein. The newly obtained effective upper bound for Huber’s constant is in the modular surface case approximately $74000$-times smaller than the previously claimed one. The degree of reduction in the case of an upper bound for Faltings’s delta function ranges from $10^{8}$ to $10^{16}$.

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