An explicit Baker-type lower bound of exponential values

Abstract

Let 𝕀 denote an imaginary quadratic field or the field ℚ of rational numbers and let ℤ 𝕀 denote its ring of integers. We shall prove a new explicit Baker-type lower bound for a ℤ 𝕀 -linear form in the numbers 1, e α 1 , . . . , e α m , m ⩾ 2, where α 0 = 0, α 1 , . . . , α m are m + 1 different numbers from the field 𝕀. Our work gives substantial improvements on the existing explicit versions of Baker’s work about exponential values at rational points. In particular, dependencies on m are improved.

Locations

• Proceedings of the Royal Society of Edinburgh Section A Mathematics - View
• arXiv (Cornell University) - View - PDF