BooksirmaMonograph

# Linear Forms in Logarithms and Applications

• ### Yann Bugeaud

Université de Strasbourg, France
Buy from \$41.00Download PDF

A subscription is required to access this book.

 Frontmatter.css-q8jq1a{padding:0;background:none;border:none;font-size:inherit;font-family:inherit;font-weight:inherit;font-family:"Source Sans Pro",sans-serif;font-weight:400;font-size:0.9em;border-radius:4px;padding:5px 10px;display:inline-block;-webkit-text-decoration:none;text-decoration:none;cursor:pointer;color:#a65a00;background-color:transparent;border:1px solid #a65a00;display:block;padding:0.3em 0.5em;margin-top:0.5em;width:-webkit-fit-content;width:-moz-fit-content;width:fit-content;font-size:0.7em;}.css-q8jq1a:disabled{opacity:0.5;cursor:not-allowed;}Download pp. i–iv PrefaceDownload pp. v–ix ContentsDownload pp. xi–xiii Frequently used notationDownload pp. xv–xvi 1 Brief introduction to linear forms in logarithms.css-ki4ov3{display:block;color:#a65a00;margin-top:0.2em;font-size:0.7em;}pp. 1–7 2 Lower bounds for linear forms in complex and .css-nii8vn .katex{font-size:1.07em;}$p$-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 $abc$-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