: 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:
: Reducing problems over general finitely generated domains to more manageable cases over number fields. Effective Results and Methods for Diophantine E...
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 . : The authors provide effective bounds for classical
: Using linear forms in logarithms of algebraic numbers to find explicit bounds. : Using linear forms in logarithms of algebraic
: The paper "Effective diophantine approximation on Gm" provides deeper insights into the underlying approximation theory used to solve these equations.
: Applying effective results from algebraic geometry and commutative algebra. Related Essential Readings
: " Exponential Diophantine Equations " by T.N. Shorey and R. Tijdeman is a foundational text focusing on the Gelfond-Baker theory.