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Article: Faber polynomials and poincaré series

TitleFaber polynomials and poincaré series
Faber polynomials and poincare series
Authors
Issue Date2011
Citation
Mathematical Research Letters, 2011, v. 18 n. 4, p. 591-611 How to Cite?
AbstractIn this paper we consider weakly holomorphic modular forms (i.e., those meromorphic modular forms for which poles only possibly occur at the cusps) of weight 2−k∈2\Z for the full modular group \SL2(\Z). The space has a distinguished set of generators f2−k,m. Such weakly holomorphic modular forms have been classified in terms of finitely many Eisenstein series, the unique weight 12 newform Δ, and certain Faber polynomials in the modular invariant j(z), the Hauptmodul for \SL2(\Z). We employ the theory of harmonic weak Maass forms and (non-holomorphic) Maass–Poincaré series in order to obtain the asymptotic growth of the coefficients of these Faber polynomials. Along the way, we obtain an asymptotic formula for the partial derivatives of the Maass–Poincaré series with respect to y as well as extending an asymptotic for the growth of the ℓth repeated integral of the Gauss error function at x to include ℓ∈\R and a wider range of x.
Persistent Identifierhttp://hdl.handle.net/10722/192197
ISSN
2015 Impact Factor: 0.523
2015 SCImago Journal Rankings: 1.444

 

DC FieldValueLanguage
dc.contributor.authorKane, Ben_US
dc.date.accessioned2013-10-23T09:27:18Z-
dc.date.available2013-10-23T09:27:18Z-
dc.date.issued2011en_US
dc.identifier.citationMathematical Research Letters, 2011, v. 18 n. 4, p. 591-611en_US
dc.identifier.issn1073-2780en_US
dc.identifier.urihttp://hdl.handle.net/10722/192197-
dc.description.abstractIn this paper we consider weakly holomorphic modular forms (i.e., those meromorphic modular forms for which poles only possibly occur at the cusps) of weight 2−k∈2\Z for the full modular group \SL2(\Z). The space has a distinguished set of generators f2−k,m. Such weakly holomorphic modular forms have been classified in terms of finitely many Eisenstein series, the unique weight 12 newform Δ, and certain Faber polynomials in the modular invariant j(z), the Hauptmodul for \SL2(\Z). We employ the theory of harmonic weak Maass forms and (non-holomorphic) Maass–Poincaré series in order to obtain the asymptotic growth of the coefficients of these Faber polynomials. Along the way, we obtain an asymptotic formula for the partial derivatives of the Maass–Poincaré series with respect to y as well as extending an asymptotic for the growth of the ℓth repeated integral of the Gauss error function at x to include ℓ∈\R and a wider range of x.-
dc.languageengen_US
dc.relation.ispartofMathematical Research Lettersen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.titleFaber polynomials and poincaré seriesen_US
dc.titleFaber polynomials and poincare series-
dc.typeArticleen_US
dc.description.naturepostprint-
dc.identifier.doi10.4310/MRL.2011.v18.n4.a2-
dc.identifier.scopuseid_2-s2.0-80051970935en_US
dc.identifier.volume18en_US
dc.identifier.issue4en_US
dc.identifier.spage591en_US
dc.identifier.epage611en_US

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