Robert A. Rankin, one of the world's foremost authorities on modular forms and a founding editor of The Ramanujan Journal, died on January 27, 2001, at the age of 85. Rankin had broad interests and contributed fundamental papers in a wide variety of areas within number theory, geometry, analysis, and algebra. To commemorate Rankin's life and work, the editors have collected together 25 papers by several eminent mathematicians reflecting Rankin's extensive range of interests within number theory. Many of these papers reflect Rankin's primary focus in modular forms. It is the...

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...