Modular Forms
ααΈα αΆ 2017 Β· American Mathematical Soc.
ααααα
βα’αα‘α·α
ααααΌαα·α
700
ααααα
α’αααΈααααα βα’αα‘α·α ααααΌαα·αααα
The theory of modular forms is a fundamental tool used in many areas of mathematics and physics. It is also a very concrete and βfunβ subject in itself and abounds with an amazing number of surprising identities.
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 AtkinβLehnerβLi theory of newforms and including the theory of Eisenstein series, RankinβSelberg 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 βgemsβ 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.
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 AtkinβLehnerβLi theory of newforms and including the theory of Eisenstein series, RankinβSelberg 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 βgemsβ 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.
The theory of modular forms is a fundamental tool used in many areas of mathematics and physics. It is also a very concrete and βfunβ subject in itself and abounds with an amazing number of surprising identities.
This comprehensive textbook, which includes numerous exercises, aims to give a com...
αααααααβα αααΎαααα
α’αααΈβα’ααααα·αααα
Henri Cohen: UniversitΓ© Bordeaux, Bordeaux, France,
Fredrik StrΓΆmberg: University of Nottingham, Nottingham, United Kingdom
Henri Cohen: UniversitΓ© Bordeaux, Bordeaux, France,
Fredrik StrΓΆmberg: University of Nottingham, Nottingham, United Kingdom
ααΆααααααααααα βα’αα‘α·α ααααΌαα·αααα
ααααΆααααΎαα’αααΈααΆααααααΎαααααα’αααα
α’αΆαβααααααΆα
ααΌαααααααααΆααα αα·αβααααααα
ααα‘αΎααααααα·ααΈ Google Play Books αααααΆαα Android αα·α iPad/iPhone α ααΆβααααΎααααΆαααααβαααααααααααααααα·ααΆαα½αβααααΈβααααα’αααβ αα·αβα’αα»ααααΆαα±ααβα’αααα’αΆααααβααΆαα’ααΈαααΊαα·α α¬ααααΆαβα’ααΈαααΊαα·αβαα
αααααααΈααααααα
αα»αααααΌαααβαα½ααα αα·ααα»αααααΌααα
α’αααα’αΆα
ααααΆααααααα
ααΆααα‘αααααααΆααα·ααα
αααα»α Google Play αααααααΎαααααα·ααΈαα»αααααΆαα’ααΈαααΊαα·ααααα»ααα»αααααΌαααααααα’αααα
eReaders αα·αβα§αααααβαααααβααα
ααΎααααΈα’αΆααα
ααΎβα§ααααα e-ink ααΌα
ααΆβα§αααααα’αΆαβααααα
α’αα‘α·α
ααααΌαα·α Kobo α’αααααΉαααααΌαβααΆαααβα―αααΆα α αΎαβαααααααΆαα
βα§αααααβααααα’αααα ααΌαα’αα»ααααααΆαβααΆαααααΆααααα’α·αααααααααααααααααα½α ααΎααααΈαααααα―αααΆαβαα
α§αααααα’αΆαααααα
βα’αα‘α·α
ααααΌαα·ααααααααΆααα
