Modular forms and functions [EBook] / Robert A. Rankin.
Modular forms and functions [EBook] / Robert A. Rankin.
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 t...
Personal Name(s):  Rankin, Robert A., (author) 

Imprint: 
Cambridge :
Cambridge University Press,
1977

Physical Description: 
1 online resource (xiii, 384 pages) 
Note: 
englisch 
ISBN: 
9780511566035 9780521091688 9780521212120 
Subject (LOC):  
Full Text 
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. 