دانلود کتاب Modular Forms: A Classical Approach

This comprehensive textbook, which includes numerous exercises, aims
to give a complete picture of the classical aspects of the subject,
with an emphasis on explicit formulas. After a number of motivating
examples such as elliptic functions and theta functions, the modular
group, its subgroups, and general aspects of holomorphic and
nonholomorphic modular forms are explained, with an emphasis on
explicit examples. The heart of the book is the classical theory
developed by Hecke and continued up to the Atkin–Lehner–Li
theory of newforms and including the theory of Eisenstein series,
Rankin–Selberg theory, and a more general theory of theta series
including the Weil representation. The final chapter explores in some
detail more general types of modular forms such as half-integral
weight, Hilbert, Jacobi, Maass, and Siegel modular forms.

Some “gems” of the book are an immediately
implementable trace formula for Hecke operators, generalizations of
Haberland’s formulas for the computation of Petersson inner products,
W. Li’s little-known theorem on the diagonalization of the
full space of modular forms, and explicit algorithms due to
the second author for computing Maass forms.

This book is essentially self-contained, the necessary tools such
as gamma and Bessel functions, Bernoulli numbers, and so on being
given in a separate chapter.

Graduate students and researchers interested in modular
forms.