The Partition Function and Modular Forms
نویسنده
چکیده
1. Intro to partition function and modular forms 1 2. Partition function leading term, without modular forms 2 3. Modular form basics 5 4. First application: Rademacher’s formula 6 4.1. A Transformation Formula for the η Function 6 4.2. Rademacher’s Convergent Series 14 5. Second application: Ramanujan congruences 22 5.1. Additional Results from Modular Functions 22 5.2. Proof of Ramanujan Congruences 23 6. Further Research on the Partition Function via Modular Forms 24 7. Acknowledgements 24 References 24
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