ETA FUNCTIONS

  • cuspmake - computes a set of inequivalent cusps for GAMMA[0](N)
  • cuspord - Computes the invariant order at a cusp of (GAMMA_0(N)) of the given etaproduct
  • cuspORD - Computes the order at a cusp z with respect to the group G= GAMMA_0(N)
  • cuspORDS - Computes the order at each cusp
  • cuspORDSnotoo - Computes the order at each cusp<> oo (GAMMA_0(N))
  • ETAchanges - changes to the ETA package
  • etaCOF -
  • etaCONSTANT - constant in eta-quotient term
  • etamult - computes the etamultiplier of eta(M tau) for a given M in SL[2](Z).
  • etanormalid - renormalize a sum of etaprods
  • etaprodcuspord - Computes the order of an eta-product at each cusp of GAMMA[0](N).
  • etaprodtoqseries2 - q-series expansion of etaproduct (omits the q^(qinf) term)
  • etaprodtoqseries - Computes q-series expansion of an eta-product
  • etaprodtoqseriesMODP - q-series expansion of etaproduct mod p
  • etaprodWe - Computes that action of W_e on a given etaproduct where W_e is an Atkin-Lehner involution of GAMMA_0(N).
  • ETApversion - package version
  • etaWe - Computes the image of an eta function eta(t tau) under the action of Atkin-Lehner involution W[ee]
  • fanwidth - fanwidth of cusp
  • Ffind - check whether on pole is at oo
  • Fricke - Fricke involution
  • gamma0FORMCHECK - checks whether modular form on GAMMA_0(N)
  • gammacheck - Checks whether an eta-product is invariant under GAMMA[0](N) (via Newman's Theorem)
  • gammacheckM - checks whether modular form on GAMMA_0(N)
  • gp2etaprod - converts a generalized permutation into an eta-product
  • GPmake - finds the GP (generalized permutation corresponding to an eta-product.
  • jacbotstar -
  • jactopstar -
  • mintotGAMMA0ORDS - lower bound for sum ORD g
  • POWERPq - q-expansion of power of q-series
  • POWERPqMODP - q-expansion of power of q-series mod p
  • POWERq - q-expansion of power of q-series
  • POWERqMODP - q-expansion of power of q-series mod p
  • printcuspords - print orders of each cusp
  • printcuspORDS - print ORDERS of each cusp
  • printETAIDORDStable - print ORDS table produced by provemodfuncGAMMA0id.
  • provemodfuncGAMMA0id - prove an eta-product identity
  • provemodfuncGAMMA0UpETAid - prove U[p] eta-product identity
  • UpLB - lower bound for ord(Up(EP),r)
  • vetainf - order at infinity of eta-quotient
  • vp - p-adic order of integer

The url of this page is http://qseries.org/fgarvan/qmaple/ETA/functions/index.html.
Created by F.G. Garvan (fgarvan@ufl.edu) on Thursday, July 11, 2013.
Last update made Sat Jun 22 14:29:40 EDT 2019.

MAIL fgarvan@ufl.edu