Title: Baker's work on linear forms in logarithms, I
Abstract: This talk is part of a series on the celebrated Baker–Heegner–Stark theorem concerning
the determination of all imaginary-quadratic number fields with class number one, following
the approach via Baker’s theorem on linear forms in logarithms of algebraic numbers. This
talk and the subsequent talk by Fabian Gundlach shall give a reasonable overview of Baker’s
1966 paper on said topic. The goal for the present talk is to present a related model problem,
following Lang (19711), and subsequently motivate the line of attack taken in Baker’s work. The
more technical aspects are deferred to the subsequent talk by Fabian Gundlach.
References
[1] A. Baker. Linear forms in the logarithms of algebraic numbers. Mathematika, 13:204–216, 1966.
[2] S. Lang. Transcendental numbers and Diophantine approximations. Bull. Amer. Math. Soc., 77(5):635–677,
1971.