What question did this study set out to answer?

The aim is to derive an explicit upper bound for the Eulerian logarithmic integral by connecting different areas of number theory.

April 27, 2026Open Access

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

Key Points

The aim is to derive an explicit upper bound for the Eulerian logarithmic integral by connecting different areas of number theory.
Applied the Baker-Matveev method for linear forms in logarithms
Focused on a primorial-based Diophantine system
Established an explicit conditional upper bound for the logarithmic integral.
Demonstrated the effective interaction between transcendental and analytic number theory.

Abstract

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.

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Cite This Study

Ahmet F. Gocgen (Sat,) studied this question.

synapsesocial.com/papers/69eefdb5fede9185760d46c6 https://doi.org/https://doi.org/10.5281/zenodo.19770928