Linear Forms in Logarithms and Applications

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	FrontmatterDownload pp. i–iv
	PrefaceDownload pp. v–ix
	ContentsDownload pp. xi–xiii
	Frequently used notationDownload pp. xv–xvi
1	Brief introduction to linear forms in logarithmspp. 1–7
2	Lower bounds for linear forms in complex and $p$ -adic logarithmspp. 9–22
3	First applicationspp. 23–45
4	Classical families of Diophantine equationspp. 47–66
5	Further applicationspp. 67–73
6	Applications of linear forms in $p$ -adic logarithmspp. 75–93
7	Primitive divisors and the greatest prime factor of $2^{n} - 1$ pp. 95–107
8	The $ab c$ -conjecturepp. 109–116
9	Simultaneous linear forms in logarithms and applicationspp. 117–123
10	Multiplicative dependence relations between algebraic numberspp. 125–129
11	Lower bounds for linear forms in two complex logarithms: proofspp. 131–141
12	Lower bounds for linear forms in two $p$ -adic logarithms: proofspp. 143–156
13	Open problemspp. 157–163
	Appendicesp. 165
A	Approximation by rational numberspp. 167–170
B	Heightspp. 171–178
C	Auxiliary results on algebraic number fieldspp. 179–182
D	Classical results on prime numberspp. 183–185
E	A zero lemmapp. 187–189
F	Tools from complex and $p$ -adic analysispp. 191–194
	Bibliographypp. 195–221
	Indexpp. 223–224