: Mathématiques: modular form

mathematical analysis > complex analysis > modular form

number > number theory > analytic number theory > modular form

mathematical analysis > functional analysis > geometry of numbers > arithmetic geometry > modular form

number > number theory > geometry of numbers > arithmetic geometry > modular form

geometry > discrete geometry > geometry of numbers > arithmetic geometry > modular form

... > real number > Diophantine approximation > geometry of numbers > arithmetic geometry > modular form

modular form

In mathematics, a modular form is a (complex) analytic function on the upper half-plane, ${\\displaystyle \\,{\\mathcal {H}}\\,}$ , that satisfies :
- a kind of functional equation with respect to the group action of the modular group,
- and a growth condition.
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.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Modular_form)

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