Problems in the Theory of Modular Forms
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Beschreibung
This book introduces the reader to the fascinating world of modular forms through a problem-solving approach. As such, besides researchers, the book can be used by the undergraduate and graduate students for self-instruction. The topics covered include q-series, the modular group, the upper half-plane, modular forms of level one and higher level, the Ramanujan τ-function, the Petersson inner product, Hecke operators, Dirichlet series attached to modular forms and further special topics. It can be viewed as a gentle introduction for a deeper study of the subject. Thus, it is ideal for non-experts seeking an entry into the field.
This book introduces the reader to the fascinating world of modular forms through a problem-solving approach. As such, besides researchers, the book can be used by the undergraduate and graduate students for self-instruction. The topics covered include q-series, the modular group, the upper half-plane, modular forms of level one and higher level, the Ramanujan τ-function, the Petersson inner product, Hecke operators, Dirichlet series attached to modular forms and further special topics. It can be viewed as a gentle introduction for a deeper study of the subject. Thus, it is ideal for non-experts seeking an entry into the field.
Introduces the fascinating world of modular forms through a problem-solving approach Discusses topics on q-series, the modular group, the upper half-plane, the Ramanujan t-function, the Petersson inner product, Hecke operators, and Dirichlet series Is authored by the winner of the Coxeter–James Prize, the Jeffery–Williams Prize, the E.W.R. Steacie Fellowship, and the Killam Fellowship
Autor*in
M. Ram Murty
Themen in »Problems in the Theory of Modular Forms«
q-series Modular Group Hecke subgroups Fundamental domains Poincar´e metric Fourier expansions valence formula Ramanujan congruences Nebentypus