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Article: Modular local polynomials

TitleModular local polynomials
Authors
Issue Date2011
PublisherInternational Press. The Journal's web site is located at http://intlpress.com/site/pub/pages/journals/items/mrl/_home/_main/
Citation
Mathematical Research Letters, 2011, v. 18, p. 10001-10011 How to Cite?
AbstractIn this paper, we consider modular local polynomials. These functions satisfy modularity while they are locally defined as polynomials outside of an exceptional set. We prove an inequality for the dimension of the space of such forms when the exceptional set is given by certain natural geodesics related to binary quadratic forms of (positive) discriminant D. We furthermore show that the dimension is the largest possible if and only if D is an even square. Following this, we describe how to use the methods developped in this paper to establish an algorithm which explicitly determines the space of modular local polynomials for each D.
Persistent Identifierhttp://hdl.handle.net/10722/208220
ISSN
2015 Impact Factor: 0.523
2015 SCImago Journal Rankings: 1.444

 

DC FieldValueLanguage
dc.contributor.authorBringmann, K-
dc.contributor.authorKane, BR-
dc.date.accessioned2015-02-23T08:08:43Z-
dc.date.available2015-02-23T08:08:43Z-
dc.date.issued2011-
dc.identifier.citationMathematical Research Letters, 2011, v. 18, p. 10001-10011-
dc.identifier.issn1073-2780-
dc.identifier.urihttp://hdl.handle.net/10722/208220-
dc.description.abstractIn this paper, we consider modular local polynomials. These functions satisfy modularity while they are locally defined as polynomials outside of an exceptional set. We prove an inequality for the dimension of the space of such forms when the exceptional set is given by certain natural geodesics related to binary quadratic forms of (positive) discriminant D. We furthermore show that the dimension is the largest possible if and only if D is an even square. Following this, we describe how to use the methods developped in this paper to establish an algorithm which explicitly determines the space of modular local polynomials for each D.-
dc.languageeng-
dc.publisherInternational Press. The Journal's web site is located at http://intlpress.com/site/pub/pages/journals/items/mrl/_home/_main/-
dc.relation.ispartofMathematical Research Letters-
dc.rightsMathematical Research Letters. Copyright © International Press.-
dc.titleModular local polynomials-
dc.typeArticle-
dc.identifier.emailKane, BR: bkane@hku.hk-
dc.identifier.authorityKane, BR=rp01820-
dc.description.naturepostprint-
dc.identifier.hkuros242472-
dc.identifier.volume18-
dc.identifier.spage10001-
dc.identifier.epage10011-
dc.publisher.placeUnited States-

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