Fricke involution

In mathematics, a Fricke involution is the involution of the modular curve X₀(N) given by τ → –1/Nτ. It is named after Robert Fricke. The Fricke involution also acts on other objects associated with the modular curve, such as spaces of modular forms and the Jacobian J₀(N) of the modular curve. The quotient of X₀(N) by the Fricke involution is a curve called X₀⁺(N), and for N prime this has genus zero only for a finite list of primes, called supersingular primes, which are the primes that divide the order of the Monster group.

See also

• Atkin–Lehner involution

References

• Iwaniec, Henryk (1997), Topics in classical automorphic forms, Graduate Studies in Mathematics, vol. 17, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-0777-4, MR 1474964