This book explores various properties of quasimodular forms, especially their connections with Jacobi-like forms and automorphic pseudodifferential operators. The material that is essential to the subject is presented in sufficient detail, including necessary background on pseudodifferential operators, Lie algebras, etc., to make it accessible also to non-specialists. The book also covers a sufficiently broad range of illustrations of how the main themes of the book have occurred in various parts of mathematics to make it attractive to a wider audience.
The book is intended for researchers and graduate students in number theory.
Author(s): Young Ju Choie, Min Ho Lee
Series: Springer Monographs in Mathematics
Publisher: Springer
Year: 2019
Language: English
Pages: 302
Front Matter ....Pages i-xv
Formal Power Series and Pseudodifferential Operators (YoungJu Choie, Min Ho Lee)....Pages 7-30
Jacobi-like Forms and Pseudodifferential Operators (YoungJu Choie, Min Ho Lee)....Pages 31-52
Hecke Operators (YoungJu Choie, Min Ho Lee)....Pages 53-76
Lie Algebras (YoungJu Choie, Min Ho Lee)....Pages 77-89
Heat Operators (YoungJu Choie, Min Ho Lee)....Pages 91-106
Group Cohomology (YoungJu Choie, Min Ho Lee)....Pages 107-120
Quasimodular Forms (YoungJu Choie, Min Ho Lee)....Pages 121-147
Quasimodular and Modular Polynomials (YoungJu Choie, Min Ho Lee)....Pages 149-164
Liftings of Quasimodular Forms (YoungJu Choie, Min Ho Lee)....Pages 165-184
Quasimodular Forms and Vector-valued Modular Forms (YoungJu Choie, Min Ho Lee)....Pages 185-206
Differential Operators on Modular Forms (YoungJu Choie, Min Ho Lee)....Pages 207-222
Half-integral Weight Forms (YoungJu Choie, Min Ho Lee)....Pages 223-234
Projective Structures (YoungJu Choie, Min Ho Lee)....Pages 235-249
Applications of Quasimodular Forms (YoungJu Choie, Min Ho Lee)....Pages 251-290
Back Matter ....Pages 291-302
