An Explicit Bound for the Logarithmic Integral Derived via Linear Forms in Logarithms

This paper establishes an explicit conditional upper bound for the Eulerian logarithmic integral by bridging transcendental and analytic number theory. Specifically, we apply the Baker-Matveev method for linear forms in logarithms to a primorial-based Diophantine system.

Keywords

Baker-Matveev method, Diophantine constraints, logarithmic integral, primorials, linear forms in logarithms, explicit upper bound

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