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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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.
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