Geometry / Seminar · 21 avril 2022

Haojie Hong [20/04/2022]

Haojie Hong (IMB)

Brief introduction to linear forms in logarithm

An expression of the form $\beta_1\log\alpha_1+\cdots+\beta_n\log\alpha_n$ is called linear form in logarithms, where $\alpha_i$ are given non-zero algebraic numbers and $\beta_j$ are variables. Alan Baker proved that if the $\log\alpha_i$ are linearly independent over the rationals, they are also linearly independent over the algebraic numbers. In this talk, I will give a concise historical introduction to the theory of linear forms in logarithms, then show some main theorems and simple applications.