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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

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
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