Effective Results And Methods For Diophantine E... Apr 2026

The "paper" you might be recalling is likely their influential 2014 journal article, published in Acta Arithmetica , which laid the groundwork for the later book.

: " Exponential Diophantine Equations " by T.N. Shorey and R. Tijdeman is a foundational text focusing on the Gelfond-Baker theory.

: The paper "Effective diophantine approximation on Gm" provides deeper insights into the underlying approximation theory used to solve these equations. Effective Results and Methods for Diophantine E...

: Using linear forms in logarithms of algebraic numbers to find explicit bounds.

: The authors provide effective bounds for classical problems including: Thue Equations : Unit Equations : in units of a domain. Hyper- and Superelliptic Equations : The Catalan Equation : Methodology : They utilize advanced techniques like: The "paper" you might be recalling is likely

: Applying effective results from algebraic geometry and commutative algebra. Related Essential Readings

The phrase you're looking for refers to a prominent field of research summarized in the book (2022) by Jan-Hendrik Evertse and Kálmán Győry . Tijdeman is a foundational text focusing on the

This work is highly regarded as the first comprehensive treatment of "effective" finiteness results—meaning the proofs don't just show that only finitely many solutions exist, but actually provide to find them. Key Content & Methods