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

By Jürgen Neukirch

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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6 (1978) 532-540; MR 58 #31007b. L. A. Bunimovich, On the ergodic properties of nowhere dispersing billiards, Commun. Math. Phys. 65 (1979) 295-312; MR 80h:58037. H. T. Croft & H. P. F. Swinnerton-Dyer, On the Steinhaus billiard table problem, Proc. Cambridge Philos. Soc. 59 (1963) 37-41; MR 26 #2925. D. W. De Temple & J. M. Robertson, A billiard path characterization of regular polygons, Math. Mag. 54 (1981) 73-75; MR 84g:52002. Unsolved Problems in Geometry 18 D. W. De Temple & J. M. Robertson, Convex curves with periodic billiard polygons, Math.

A related problem appears in Melzak's collection, where it is required to find the shortest path whose convex hull approximates a convex surface to within e. Z. A. Melzak, Problems connected with convexity, Problem 39, Canad. Math. Bull. 8 (1965) 565-573; MR 33 #4781. A30. The shortest curve cutting all the lines through a disk. Croft considered the problem of finding the shortest curve in the plane that cuts every chord (produced both ways) of a fixed disk K of unit radius.

Bieri, Mitteilung zum Problem eines konvexen Extremalkorpers, Arch. Math. (Basel) 1 (1949) 462-463; MR ll, 127. H. Groemer, Eine neue Ungleichung fiir konvexe Korper, Math. Z. 86 (1985) 361-364. H. Hadwiger, P. Glur & H. Bieri, Die symmetrische Kugelzone als extremale Rotationskorper, Experientia 4 (1948) 304-305; MR 10, 141. H. Hadwiger, Elementare Studie iiber konvexe Rotationskorper, Mat h. N achr. 2 (1949) 114-123; MR 11,127. H. Hadwiger, [Had], Section 28. H. Hadwiger, Notiz fiir fehlenden Ungleichung in der Theorie der konvexen Korper, Elem.

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