logarithm

A newly shared preprint claims to prove that logarithms of rational numbers have irrationality exponent 2, a measure of how well such numbers can be approximated by rationals. The result would sharpen known bounds for numbers like log 2. The paper is circulating among mathematicians, with early discussion focused on verifying the argument and assessing whether the proof holds up.

A new paper by GitHub user jdb1729 proves that the logarithms of rational numbers have irrationality exponent exactly 2, meaning they cannot be approximated by rationals much better than generic irrational numbers. The result, shared as a self-published PDF, is drawing attention from mathematically inclined readers who are discussing the proof techniques and how the bound compares to known results for related constants.