Theorie der Modulfunktionen. Erster Teil der Vorlesung: Über den Picard schen Satz …

LANDAU, Edmund

Verlag: N.p. [Berlin?], 1905

Beschreibung

Folio, ff. [40]; typescript; mathematical equations inserted in black ink; five leaves with diagrams on verso, three as paste-ons; a very good copy in contemporary cloth-backed boards; from the library of Hans Georg Joseph, with his Archimedian bookplate in Art Nouveau style by Franz Stassen (1896-1949).AN ANNOTATED TYPESCRIPT OF LANDAU S IMPORTANT LECTURE ON PICARD S THEOREM. In 1879 Émile Picard proved that a meromorphic function which omits more than two values is a constant. This theorem was justly hailed as an outstanding achievement and for many years it stirred the imagination of many prominent mathematicians with results that were ultimately epoch making. Picard s proof was based on the elliptic modular function, a theory which was in the center of analysis at that time. Toward the end of the nineteenth century, mathematicians tried to replace Picard s method by more elementary considerations, and in 1896 Émile Borel succeeded in giving such a proof. In the able hands of Edmund Landau this proof gave in 1904 some astonishing results concerning the influence of the first two coefficients of a power series on the properties of a function defined by the series. These results were taken as a vindication of the elementary methods, but the triumph was brief, for in 1905 Constantin Carathéodory proved that the modular function played the role of extremal function in Landau s problem (Einar Hille, Analytic Function Theory, p. 219). Bestandsnummer des Verkäufers 352268a744a686140f210459667904d4

Bibliografische Details

Titel: Theorie der Modulfunktionen. Erster Teil der...

Verlag: N.p. [Berlin?]

Erscheinungsdatum: 1905

Einband: Hardcover

Zustand: Very Good