Mock Modular Forms

Mock modular forms are special mathematical functions that resemble modular forms but do not fully meet all their symmetry properties. They were originally discovered in the context of number theory and string theory. Unlike true modular forms, which transform predictably under certain geometric transformations, mock modular forms have a "shadow" component that corrects their behavior, making them part of a broader, richer structure. They have applications in understanding black hole entropy, partition functions, and combinatorics, bridging the gap between classical modular forms and more complex, real-world phenomena.