Modular Forms
Cusp forms, Hecke operators, and the Eichler–Shimura correspondence.
Modular Forms. Cusp forms, Hecke operators, and the Eichler–Shimura correspondence.
Foundations and canonical references
The standard treatments of modular forms approach the subject from complementary angles. Diamond, A First Course in Modular Forms (2005) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Open methodological questions for modular forms include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2005A First Course in Modular Formsdiamond-2005, shurman-2005
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