02010nam a22003375a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084001500184100002800199245008700227260008200314300003400396336002600430337002600456338003600482347002400518490008300542506006500625520083500690650002601525650002301551856003201574856006601606228-180207CH-001817-320180207233003.0a fot ||| 0|cr nn mmmmamaa180207e20180314sz fot ||| 0|eng d a978303719683070a10.4171/1832doi ach0018173 7aPBR2bicssc a11-xx2msc1 aBugeaud, Yann,eauthor.10aLinear Forms in Logarithms and Applicationsh[electronic resource] /cYann Bugeaud3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2018 a1 online resource (240 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v281 aRestricted to subscribers:uhttp://www.ems-ph.org/ebooks.php aThe aim of this book is to serve as an introductory text to the theory of linear forms in the logarithms of algebraic numbers, with a special emphasis on a large variety of its applications. We wish to help students and researchers to learn what is hidden inside the blackbox ‚Baker's theory of linear forms in logarithms' (in complex or in \$p\$-adic logarithms) and how this theory applies to many Diophantine problems, including the e ffective resolution of Diophantine equations, the \$abc\$-conjecture, and upper bounds for the irrationality measure of some real numbers. Written for a broad audience, this accessible and self-contained book can be used for graduate courses (some 30 exercises are supplied). Specialists will appreciate the inclusion of over 30 open problems and the rich bibliography of over 450 references.07aNumber theory2bicssc07aNumber theory2msc40uhttps://doi.org/10.4171/183423cover imageuhttp://www.ems-ph.org/img/books/bugeaud_mini.jpg