Number Theory III (e-bog) af Lang, Serge
Lang, Serge (forfatter)

Number Theory III e-bog

875,33 DKK (inkl. moms 1094,16 DKK)
In 1988 Shafarevich asked me to write a volume for the Encyclopaedia of Mathematical Sciences on Diophantine Geometry. I said yes, and here is the volume. By definition, diophantine problems concern the solutions of equations in integers, or rational numbers, or various generalizations, such as finitely generated rings over Z or finitely generated fields over Q. The word Geometry is tacked on t...
E-bog 875,33 DKK
Forfattere Lang, Serge (forfatter), Lang, Serge (redaktør)
Forlag Springer
Udgivet 1 december 2013
Genrer PBH
Sprog English
Format pdf
Beskyttelse LCP
ISBN 9783642582271
In 1988 Shafarevich asked me to write a volume for the Encyclopaedia of Mathematical Sciences on Diophantine Geometry. I said yes, and here is the volume. By definition, diophantine problems concern the solutions of equations in integers, or rational numbers, or various generalizations, such as finitely generated rings over Z or finitely generated fields over Q. The word Geometry is tacked on to suggest geometric methods. This means that the present volume is not elementary. For a survey of some basic problems with a much more elementary approach, see [La 9Oc]. The field of diophantine geometry is now moving quite rapidly. Out- standing conjectures ranging from decades back are being proved. I have tried to give the book some sort of coherence and permanence by em- phasizing structural conjectures as much as results, so that one has a clear picture of the field. On the whole, I omit proofs, according to the boundary conditions of the encyclopedia. On some occasions I do give some ideas for the proofs when these are especially important. In any case, a lengthy bibliography refers to papers and books where proofs may be found. I have also followed Shafarevich's suggestion to give examples, and I have especially chosen these examples which show how some classical problems do or do not get solved by contemporary in- sights. Fermat's last theorem occupies an intermediate position. Al- though it is not proved, it is not an isolated problem any more.