This book provides an introduction to the theory of elliptic modular functions and forms, a subject of increasing interest because of its connexions with the theory of elliptic curves. Modular forms are generalisations of functions like theta functions. They can be expressed as Fourier series, and the Fourier coefficients frequently possess multiplicative properties which lead to a correspondence between modular forms and Dirichlet series having Euler products. The Fourier coefficients also arise in certain representational problems in the theory of numbers, for example in the study of the number of ways in which a positive integer may be expressed as a sum of a given number of squares. The treatment of the theory presented here is fuller than is customary in a textbook on automorphic or modular forms, since it is not confined solely to modular forms of integral weight (dimension). It will be of interest to professional mathematicians as well as senior undergraduate and graduate students in pure mathematics.
Sprache
Verlagsort
Zielgruppe
Produkt-Hinweis
Illustrationen
Worked examples or Exercises
Maße
Höhe: 229 mm
Breite: 152 mm
Dicke: 23 mm
Gewicht
ISBN-13
978-0-521-09168-8 (9780521091688)
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Schweitzer Klassifikation
1. Groups of matrices and bilinear mappings; 2. Mapping properties; 3. Automorphic factors and multiplier systems; 4. General properties of modular forms; 5. Construction of modular forms; 6. Functions belonging to the full modular group; 7. Groups of level 2 and sums of squares; 8. Modular forms of level N; 9. Hecke operators and congruence groups; 10. Applications.
