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Problems in the Theory of Modular Forms

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-pla...

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Bibliographic Details
Main Authors: Murty, M. Ram, Dewar, Michael (Author), Graves, Hester (Author)
Format: eBook
Language:English
Published: Singapore Springer Nature Singapore 2016, 2016
Edition:1st ed. 2016
Series:IMSc Lecture Notes in Mathematics
Subjects:
Number Theory
Special Functions
Sequences, Series, Summability
Operator Theory
Sequences (mathematics)
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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245 0 0 |a Problems in the Theory of Modular Forms  |h Elektronische Ressource  |c by M. Ram Murty, Michael Dewar, Hester Graves 
250 |a 1st ed. 2016 
260 |a Singapore  |b Springer Nature Singapore  |c 2016, 2016 
300 |a XVII, 291 p. 8 illus  |b online resource 
505 0 |a Part I Problems -- Chapter 1. Jacobi’s q-series -- Chapter 2. The Modular Group -- Chapter 3. The Upper Half-Plane -- Chapter 4. Modular Forms of Level One -- Chapter 5. The Ramanujan _ T-function -- Chapter 6. Modular Forms of Higher Level -- Chapter 7. The Petersson Inner Product -- Chapter 8. Hecke Operators of Higher Level -- Chapter 9. Dirichlet Series and Modular Forms -- Chapter 10. Special Topics -- Part II Solutions -- Chapter 1. Jacobi’s q-series -- Chapter 2. The Modular Group -- Chapter 3. The Upper Half-Plane -- Chapter 4. Modular Forms of Level One -- Chapter 5. The Ramanujan _ T-function -- Chapter 6. Modular Forms of Higher Level -- Chapter 7. The Petersson Inner Product -- Chapter 8. Hecke Operators of Higher Level -- Chapter 9. Dirichlet Series and Modular Forms -- Chapter 10. Special Topics 
653 |a Number theory 
653 |a Special Functions 
653 |a Number Theory 
653 |a Sequences, Series, Summability 
653 |a Operator theory 
653 |a Operator Theory 
653 |a Sequences (Mathematics) 
653 |a Special functions 
700 1 |a Dewar, Michael  |e [author] 
700 1 |a Graves, Hester  |e [author] 
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989 |b Springer  |a Springer eBooks 2005- 
490 0 |a IMSc Lecture Notes in Mathematics 
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856 4 0 |u https://doi.org/10.1007/978-981-10-2651-5?nosfx=y  |x Verlag  |3 Volltext 
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520 |a 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. 

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