Buch, Englisch, Band 1752, 260 Seiten, Format (B × H): 155 mm x 233 mm, Gewicht: 420 g
Reihe: Lecture Notes in Mathematics
Buch, Englisch, Band 1752, 260 Seiten, Format (B × H): 155 mm x 233 mm, Gewicht: 420 g
Reihe: Lecture Notes in Mathematics
ISBN: 978-3-540-41496-4
Verlag: Springer Berlin Heidelberg
In the last five years there has been very significant progress in the development of transcendence theory. A new approach to the arithmetic properties of values of modular forms and theta-functions was found. The solution of the Mahler-Manin problem on values of modular function j(tau) and algebraic independence of numbers pi and e^(pi) are most impressive results of this breakthrough. The book presents these and other results on algebraic independence of numbers and further, a detailed exposition of methods created in last the 25 years, during which commutative algebra and algebraic geometry exerted strong catalytic influence on the development of the subject.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
?(?, z) and Transcendence.- Mahler’s conjecture and other transcendence Results.- Algebraic independence for values of Ramanujan Functions.- Some remarks on proofs of algebraic independence.- Elimination multihomogene.- Diophantine geometry.- Géométrie diophantienne multiprojective.- Criteria for algebraic independence.- Upper bounds for (geometric) Hilbert functions.- Multiplicity estimates for solutions of algebraic differential equations.- Zero Estimates on Commutative Algebraic Groups.- Measures of algebraic independence for Mahler functions.- Algebraic Independence in Algebraic Groups. Part 1: Small Transcendence Degrees.- Algebraic Independence in Algebraic Groups. Part II: Large Transcendence Degrees.- Some metric results in Transcendental Numbers Theory.- The Hilbert Nullstellensatz, Inequalities for Polynomials, and Algebraic Independence.
