An explicit Baker-type lower bound of exponential values

Anne-Maria Ernvall-Hytönen, Kalle Leppälä, Tapani Matala-aho
2015 Proceedings of the Royal Society of Edinburgh. Section A Mathematics  
Let 𝕀 denote an imaginary quadratic field or the field ℚ of rational numbers and let ℤ𝕀denote its ring of integers. We shall prove a new explicit Baker-type lower bound for a ℤ𝕀-linear form in the numbers 1, eα1, . . . , eαm,m⩾ 2, whereα0= 0,α1, . . . ,αmarem+ 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 onmare improved.
doi:10.1017/s0308210515000049 fatcat:ptqmxiu5ojezvahb2qzwbwkco4