In
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, a Fricke involution is the
involution
Involution may refer to:
* Involute, a construction in the differential geometry of curves
* '' Agricultural Involution: The Processes of Ecological Change in Indonesia'', a 1963 study of intensification of production through increased labour inpu ...
of the
modular curve
In number theory and algebraic geometry, a modular curve ''Y''(Γ) is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of the complex upper half-plane H by the action of a congruence subgroup Γ of the modular ...
''X''
0(''N'') given by τ → –1/''N''τ. It is named after
Robert Fricke
Karl Emanuel Robert Fricke (24 September 1861 – 18 July 1930) was a German mathematician, known for his work in complex analysis, especially on elliptic, modular and automorphic functions. He was one of the main collaborators of Felix Kle ...
. The Fricke involution also acts on other objects associated with the modular curve, such as spaces of
modular forms and the
Jacobian ''J''
0(''N'') of the modular curve.
See also
*
Atkin–Lehner involution
References
*
Modular forms
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