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Concept
Modular Form
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Summary
A
Modular Form
is a
Complex analytic function
on the
Upper Half-plane
that is invariant under the action of a
Discrete Subgroup
of SL(2, ℝ), typically satisfying additional
Growth Conditions
at infinity. These functions play a crucial role in
Number Theory
, particularly in the theory of
Elliptic Curves
, and have applications in physics, such as
String Theory
and
Conformal Field Theory
.
Concepts
Elliptic Curves
SL(2, ℝ)
Complex Analysis
Discrete Subgroups
Upper Half-plane
Modular Group
Fourier Series
Automorphic Forms
Hecke Operators
L-functions
Riemann Surfaces
Cusp Forms
Fuchsian Groups
Abelian Variety
Relevant Degrees
Algebra 100%
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