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Article: Modular local polynomials
Title | Modular local polynomials |
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Authors | |
Issue Date | 2016 |
Publisher | International Press. The Journal's web site is located at http://intlpress.com/site/pub/pages/journals/items/mrl/_home/_main/ |
Citation | Mathematical Research Letters, 2016, v. 23, p. 973-987 How to Cite? |
Abstract | In 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 Identifier | http://hdl.handle.net/10722/208220 |
ISSN | 2023 Impact Factor: 0.6 2023 SCImago Journal Rankings: 1.128 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Bringmann, K | - |
dc.contributor.author | Kane, BR | - |
dc.date.accessioned | 2015-02-23T08:08:43Z | - |
dc.date.available | 2015-02-23T08:08:43Z | - |
dc.date.issued | 2016 | - |
dc.identifier.citation | Mathematical Research Letters, 2016, v. 23, p. 973-987 | - |
dc.identifier.issn | 1073-2780 | - |
dc.identifier.uri | http://hdl.handle.net/10722/208220 | - |
dc.description.abstract | In 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.language | eng | - |
dc.publisher | International Press. The Journal's web site is located at http://intlpress.com/site/pub/pages/journals/items/mrl/_home/_main/ | - |
dc.relation.ispartof | Mathematical Research Letters | - |
dc.rights | Mathematical Research Letters. Copyright © International Press. | - |
dc.title | Modular local polynomials | - |
dc.type | Article | - |
dc.identifier.email | Kane, BR: bkane@hku.hk | - |
dc.identifier.authority | Kane, BR=rp01820 | - |
dc.description.nature | postprint | - |
dc.identifier.doi | 10.4310/MRL.2016.v23.n4.a2 | - |
dc.identifier.scopus | eid_2-s2.0-84989879374 | - |
dc.identifier.hkuros | 242472 | - |
dc.identifier.volume | 23 | - |
dc.identifier.spage | 973 | - |
dc.identifier.epage | 987 | - |
dc.identifier.isi | WOS:000391192400002 | - |
dc.publisher.place | United States | - |
dc.identifier.issnl | 1073-2780 | - |