Overview

Die Theorie der elliptischen Funktionen und Modulformen wird in der englischsprachigen Literatur im allgemeinen auf sehr hohem Niveau abgehandelt. Den Autoren ist es gelungen, eine Brücke von den elementaren Grundlagen zum aktuellen Forschungsstand zu schlagen. Ausgehend von den Weierstraßschen Arbeiten werden auch elliptische Kurven und komplexe Multiplikation behandelt. Der Teil über elliptische Modulformen ist auch separat lesbar und enthält neben Fundamentalbereichen und Dimensionsbestimmung auch ein Kapitel über Hecke-Operatoren und Dirichlet-Reihen mit Funktionalgleichung. Großes Gewicht wird auf Theta-Reihen gelegt. Erstmals in Lehrbuchform wird ein Beweis des Siegelschen Hauptsatzes für elliptische Modulformen gegeben. Ausführliche Beweise und zahlreiche Übungsaufgaben zeichnen dieses Buch besonders aus.

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9783540493242

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<p>From the reviews of the second edition: <p><p> The book under review is the basically unaltered second edition of the original, whose popularity at German-speaking universities has grown continually over the past decade. Altogether, the present second edition of this well-established, highly cultured textbook on elliptic functions and modular forms comes with remarkable and appropriate improvements, amplifications, and up-datings. this text breathes the inimitable spirit of the late Max Koecher, a great mathematical researcher and teacher, and his co-author 's effort at communicating and preserving it must be highly acknowledged. (Werner Kleinert, Zentralblatt MATH, Vol. 1129 (7), 2008)

From the reviews of the second edition: The book under review is the basically unaltered second edition of the original, whose popularity at German-speaking universities has grown continually over the past decade. Altogether, the present second edition of this well-established, highly cultured textbook on elliptic functions and modular forms comes with remarkable and appropriate improvements, amplifications, and up-datings. this text breathes the inimitable spirit of the late Max Koecher, a great mathematical researcher and teacher, and his co-author s effort at communicating and preserving it must be highly acknowledged. (Werner Kleinert, Zentralblatt MATH, Vol. 1129 (7), 2008) The book provides an introduction to elliptic functions . The presentation is excellent: the book always carefully lays the foundations and from there proceeds to substantial results while always giving complete arguments. (J. Mahnkopf, Monatshefte fur Mathematik, Vol. 156 (3), March, 2009)

From the reviews of the second edition: The book under review is the basically unaltered second edition of the original, whose popularity at German-speaking universities has grown continually over the past decade. ... Altogether, the present second edition of this well-established, highly cultured textbook on elliptic functions and modular forms comes with ... remarkable and appropriate improvements, amplifications, and up-datings. ... this text breathes the inimitable spirit of the late Max Koecher, a great mathematical researcher and teacher, and his co-author's effort at communicating and preserving it must be highly acknowledged. (Werner Kleinert, Zentralblatt MATH, Vol. 1129 (7), 2008) The book provides an introduction to elliptic functions ... . The presentation is excellent: the book always carefully lays the foundations and from there proceeds to substantial results ... while always giving complete arguments. (J. Mahnkopf, Monatshefte fur Mathematik, Vol. 156 (3), March, 2009)

From the reviews of the second edition: The book under review is the basically unaltered second edition of the original, whose popularity at German-speaking universities has grown continually over the past decade. ... Altogether, the present second edition of this well-established, highly cultured textbook on elliptic functions and modular forms comes with ... remarkable and appropriate improvements, amplifications, and up-datings. ... this text breathes the inimitable spirit of the late Max Koecher, a great mathematical researcher and teacher, and his co-author's effort at communicating and preserving it must be highly acknowledged. (Werner Kleinert, Zentralblatt MATH, Vol. 1129 (7), 2008) The book provides an introduction to elliptic functions ... . The presentation is excellent: the book always carefully lays the foundations and from there proceeds to substantial results ... while always giving complete arguments. (J. Mahnkopf, Monatshefte fur Mathematik, Vol. 156 (3), March, 2009)

From the reviews of the second edition: <p> The book under review is the basically unaltered second edition of the original, whose popularity at German-speaking universities has grown continually over the past decade. a ] Altogether, the present second edition of this well-established, highly cultured textbook on elliptic functions and modular forms comes with a ] remarkable and appropriate improvements, amplifications, and up-datings. a ] this text breathes the inimitable spirit of the late Max Koecher, a great mathematical researcher and teacher, and his co-authora (TM)s effort at communicating and preserving it must be highly acknowledged. (Werner Kleinert, Zentralblatt MATH, Vol. 1129 (7), 2008)

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