Open AccessEffective bounds for Huber’s constant and Faltings’s delta function
Author(s) -
Muharem Avdispahić
Publication year - 2021
Publication title -
mathematics of computation
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.95
H-Index - 103
eISSN - 1088-6842
pISSN - 0025-5718
DOI - 10.1090/mcom/3631
Subject(s) - algorithm , annotation , type (biology) , mathematics , function (biology) , artificial intelligence , computer science , database , geology , paleontology , evolutionary biology , biology
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} .