ETA FUNCTIONS

• cuspmake - computes a set of inequivalent cusps for GAMMA[0](N)
• 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 -
• etacombo2ETAPRODlist - Convert etacombo to a list of eta-products
• etacombo2ETAPRODwCONSlist - Convert etacombo to a list of eta-products with constants
• 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).
• etaprodtoqseries - Computes q-series expansion of an eta-product
• etaprodtoqseries2 - q-series expansion of etaproduct (omits the q^(qinf) term)
• 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
• printETAIDORDStable - print ORDS table produced by provemodfuncGAMMA0id.
• provemodfuncGAMMA0id - prove an eta-product identity
• provemodfuncGAMMA0idBATCH - proving etaid as a modfunc on Gamma0(N)
• provemodfuncGAMMA0UpETAid - prove U[p] eta-product identity
• provemodfuncGAMMA0UpETAidBATCH - prove U[p] eta-product identity
• qetacombo - q-expansion of a symbolic linear combo of eta-products
• 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 https://qseries.org/fgarvan/qmaple/ETA/eta-0p3bfunctions/index.html.
Created by F.G. Garvan (fgarvan@ufl.edu) on Thursday, July 11, 2013.
Last update made Sun Jun 30 16:49:18 EDT 2019.

fgarvan@ufl.edu