Huber常数和Faltings函数的有效界

Math. Comput. Model. Pub Date : 2021-03-24 DOI:10.1090/MCOM/3631

Muharem Avdispahić

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摘要

通过对第一类有限Fuchsian群上与素数测地线定理有关的Friedman-Jorgenson-Kramer算法的仔细考察，我们改进了其中的常数。在模曲面情况下，新得到的Huber常数的有效上界比之前的有效上界小约74000 74000倍。法尔廷斯函数的上界的简化程度从10 8 10^{8}到10 16 10^{16}。

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

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 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 10^{8} to 10 16 10^{16} .

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Math. Comput. Model.

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