Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function e^z. A central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. This book includes proofs of the main basic results (theorems of Hermite-Lindemann, Gelfond-Schneider, 6 exponentials theorem), an introduction to height functions with a discussion of Lehmer's problem, several proofs of Baker's theorem as well as explicit measures of linear independence of logarithms. An original feature is that proofs make systematic use of Laurent's interpolation determinants. The most general result is the so-called Theorem of the Linear Subgroup, an effective version of which is also included. It yields new results of simultaneous approximation and of algebraic independence. 2 chapters written by D. Roy provide complete and at the same time simplified proofs of zero estimates (due to P. Philippon) on linear algebraic groups

Approximatie [Diophantische ] --- Approximation [Diophantienne ] --- Approximation [Diophantine ] --- Diophantine approximation --- Groupes algébraïques linéaires --- Lineaire algebraïsche groepen --- Linear algebraic groups --- Diophantine approximation. --- Linear algebraic groups. --- 512.74 --- Algebraic groups, Linear --- Geometry, Algebraic --- Group theory --- Algebraic varieties --- Approximation, Diophantine --- Approximation theory --- Diophantine analysis --- Algebraic groups. Abelian varieties --- 512.74 Algebraic groups. Abelian varieties --- Mathematics --- Number theory --- Mathématiques --- Géométrie algébrique --- Théorie des groupes --- Théorie des nombres --- Algebra. --- Number theory. --- Algebraic geometry. --- Group theory. --- Number Theory. --- Algebraic Geometry. --- Group Theory and Generalizations. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Algebraic geometry --- Geometry --- Number study --- Numbers, Theory of --- Mathematical analysis

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Number theory --- Group theory

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Various developments in physics have involved many questions related to number theory, in an increasingly direct way. This trend is especially visible in two broad families of problems, namely, field theories, and dynamical systems and chaos. The 14 chapters of this book are extended, self-contained versions of expository lecture courses given at a school on "Number Theory and Physics" held at Les Houches for mathematicians and physicists. Most go as far as recent developments in the field. Some adapt an original pedagogical viewpoint.

Number theory --- Mathematical physics --- Théorie des nombres --- Physique mathématique --- Congresses --- Congrès --- -Number theory --- 51-7 --- 511 --- 511.6 --- -#TELE:MI2 --- 511.6 Algebraic number fields --- Algebraic number fields --- 511 Number theory --- 51-7 Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc. --- Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc. --- Number study --- Numbers, Theory of --- Algebra --- Physical mathematics --- Physics --- Mathematics --- Congresses. --- Mathematical physics - Congresses --- Number theory - Congresses --- -Congresses

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Nombres, Théorie des

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)