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.

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A question on FLT and Taniyama Shimura

Sometime back i watched the documentary of Andrew Wiles proving the Fermat's Last theorem. A truly inspiring video and i still watch it whenever i am in a depressed mood. There are certain ...
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Definition of cusp of a congruence group

I am reading p.22 of Dan Bump's Automorphihic forms and representations. A cusp of the congruence group acting on the upper half plane is defined to be an orbit of the action of the congruence ...