Buch, Englisch, Band 79, 268 Seiten
Buch, Englisch, Band 79, 268 Seiten
Reihe: Graduate Studies in Mathematics
ISBN: 978-0-8218-3960-7
Verlag: American Mathematical Society
This marvellous and highly original book fills a significant gap in the extensive literature on classical modular forms. This is not just yet another introductory text to this theory, though it could certainly be used as such in conjunction with more traditional treatments. Its novelty lies in its computational emphasis throughout: Stein not only defines what modular forms are, but shows in illuminating detail how one can compute everything about them in practice. This is illustrated throughout the book with examples from his own (entirely free) software package SAGE, which really bring the subject to life while not detracting in any way from its theoretical beauty. The author is the leading expert in computations with modular forms, and what he says on this subject is all tried and tested and based on his extensive experience. As well as being an invaluable companion to those learning the theory in a more traditional way, this book will be a great help to those who wish to use modular forms in appl --John E. Cremona, University of Nottingham William Stein is an associate professor of mathematics at the University of Washington at Seattle. He earned a PhD in mathematics from UC Berkeley and has held positions at Harvard University and UC San Diego. His current research interests lie in modular forms, elliptic curves, and computational mathematics.
Zielgruppe
Graduate students and research mathematicians interested in modular forms.
Autoren/Hrsg.
Weitere Infos & Material
Modular forms
Modular forms of level $1$
Modular forms of weight $2$
Dirichlet characters
Eisenstein series and Bernoulli numbers
Dimension formulas
Linear algebra
General modular symbols
Computing with newforms
Computing periods
Solutions to selected exercises
Appendix A: Computing in higher rank
Bibliography
Index
