Download PDF by Jürgen Neukirch: Algebraische Zahlentheorie (Springer-Lehrbuch Masterclass)

By Jürgen Neukirch

ISBN-10: 3540375473

ISBN-13: 9783540375470

Algebraische Zahlentheorie: eine der traditionsreichsten und aktuellsten Grunddisziplinen der Mathematik. Das vorliegende Buch schildert ausführlich Grundlagen und Höhepunkte. Konkret, glossy und in vielen Teilen neu. Neu: Theorie der Ordnungen. Plus: die geometrische Neubegründung der Theorie der algebraischen Zahlkörper durch die "Riemann-Roch-Theorie" vom "Arakelovschen Standpunkt", die bis hin zum "Grothendieck-Riemann-Roch-Theorem" führt.

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Extra resources for Algebraische Zahlentheorie (Springer-Lehrbuch Masterclass)

Example text

Functions and the Koch i n f i n i t e d e t e r m i n a n t The Koch's method of infinite determinants c l o s e l y c o n n e c t e d w i t h the method of Hill's d e t e r m i n a n t s is [26], repre- senting the c h a r a c t e r i s t i c numbers of solutions of equations with the periodic process coefficients. of finding of The relationship Floquet exponents between for e q u a t i o n s w i t h p e r i o d i c c o e f f i c i e n t s and the d e t e r m i n a t i o n of the invariants ture, of the m o n o d r o m y group was d e s c r i b e d in the classical see p a r t i c u l a r l y [5], ship was p r e s e n t e d by Magnus [31], [72] [71].

6). to g e n e r a t e parameter h. two Let us put: l(n-2r) (n+2r+l)k2Xr - [H-4(r+l) 2 (2-k 2 ) ] x r + 1 + ~(n-2r-3) (n+2r+4)k2Xr+2 = 0: r = 1 ....

S u f f i c i e n t conditions take longer time to check, on the size of (see parti- The since k n o w n bounds (see [46]). One expects m a x P to be r e l a t i v e l y small, but in the similar and related s i t u a t i o n of C h e b o r a t e f f ' s [46], theorem (cf. [49]) the best bounds on max P are a c h i e v e d only assuming the R i e m a n n hypothesis. 2: The second r e d u c i b i l i t y p r o b l e m is even more geometric. a p r o b l e m of r e d u c t i o n of A b e l i a n integrals to a smaller genus.

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Algebraische Zahlentheorie (Springer-Lehrbuch Masterclass) by Jürgen Neukirch

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