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What area of math are modular forms?

The theory of modular forms therefore belongs to complex analysis. The main importance of the theory is its connections with number theory. Modular forms appear in other areas, such as algebraic topology, sphere packing, and string theory.

What is an example of a modular form?

This writeup gives first examples of modular forms: Eisenstein series, the dis- criminant, and the j-function. The modular group is the group of 2-by-2 matrices with integer entries and determinant 1, SL2(Z) = {[ a b c d ] : a, b, c, d Z, ad bc = 1 } . c d ] () = a + b c + d , ̂C.

What are the prerequisites for modular arithmetic?

Prerequisite knowledge/skills Students should be able to perform basic operations (addition, subtraction, multiplication, division) and have an understanding of basic Algebra. Students should also understand what the basic number systems are and how they differ.

What is the order of modular form?

The order of a modular form is invariant under the action of SL2(Z) is nonvanishing and holomorphic at p.

What are the prerequisites for automorphic forms?

Automorphic forms are special functions on the adlic points of an algebraic group, so to get started, you would need: Knowledge of algebraic groups. This includes structure theory of reductive groups, which in turn relies on a good deal of algebraic geometry.

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