# Modular form

analytic function on the upper half-plane with a certain behavior under the modular group

In mathematics, a **modular form** is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition.

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## Quotes edit

- Modular forms have long played a key role in the theory of numbers, including most famously the proof of Fermat's Last Theorem.
- Noriko Yui, Helena Verrill, and Charles F. Doran.
*Modular Forms and String Duality*. American Mathematical Society. p. 9. ISBN 978-0-8218-7157-7.

- Noriko Yui, Helena Verrill, and Charles F. Doran.