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Modular Forms by Mahesh Kakde
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- 1 Modular Forms
- 2 Definition of Seegel Modular Forms?
- 3 What are called Elliptic Modular Forms?
- 4 Remark
- 5 Congruence Subgroups
- 6 What Cusps are?
- 7 Fourier Expansion
- 8 Example - Explicitly in terms of coefficients
- 9 Remark of SL2Z modulo plus minus 1
- 10 Theorem
- 11 Fundamental Domain
- 12 Gauss's Theorem
- 13 Eisenstein series
- 14 Proposition and dimension formula
- 15 Sketch
- 16 Eisenstein series of out 2
- 17 Proposition
- 18 Proof - Hecker's trick
- 19 Holomorphic modular forms
- 20 Differential operators
- 21 Proposition
- 22 Sketch
- 23 More examples
- 24 Theta series
- 25 Proposition
- 26 Sketch
- 27 Extremal practices
