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Article: Representations of integers by ternary quadratic forms

TitleRepresentations of integers by ternary quadratic forms
Authors
KeywordsQuaternion algebra
Elliptic curves
Maximal orders
Half-integer weight modular forms
Kohnen's plus space
Shimura lifts
Issue Date2010
Citation
International Journal of Number Theory, 2010, v. 6 n. 1, p. 127-158 How to Cite?
AbstractWe investigate the representation of integers by quadratic forms whose theta series lie in Kohnen's plus space , where p is a prime. Conditional upon certain GRH hypotheses, we show effectively that every sufficiently large discriminant with bounded divisibility by p is represented by the form, up to local conditions. We give an algorithm for explicitly calculating the bounds. For small p, we then use a computer to find the full list of all discriminants not represented by the form. Finally, conditional upon GRH for L-functions of weight 2 newforms, we give an algorithm for computing the implied constant of the Ramanujan–Petersson conjecture for weight 3/2 cusp forms of level 4N in Kohnen's plus space with N odd and squarefree.
Persistent Identifierhttp://hdl.handle.net/10722/192191
ISSN
2015 Impact Factor: 0.463
2015 SCImago Journal Rankings: 0.761
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorKane, Ben_US
dc.date.accessioned2013-10-23T09:27:17Z-
dc.date.available2013-10-23T09:27:17Z-
dc.date.issued2010en_US
dc.identifier.citationInternational Journal of Number Theory, 2010, v. 6 n. 1, p. 127-158en_US
dc.identifier.issn1793-0421en_US
dc.identifier.urihttp://hdl.handle.net/10722/192191-
dc.description.abstractWe investigate the representation of integers by quadratic forms whose theta series lie in Kohnen's plus space , where p is a prime. Conditional upon certain GRH hypotheses, we show effectively that every sufficiently large discriminant with bounded divisibility by p is represented by the form, up to local conditions. We give an algorithm for explicitly calculating the bounds. For small p, we then use a computer to find the full list of all discriminants not represented by the form. Finally, conditional upon GRH for L-functions of weight 2 newforms, we give an algorithm for computing the implied constant of the Ramanujan–Petersson conjecture for weight 3/2 cusp forms of level 4N in Kohnen's plus space with N odd and squarefree.-
dc.languageengen_US
dc.relation.ispartofInternational Journal of Number Theoryen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectQuaternion algebra-
dc.subjectElliptic curves-
dc.subjectMaximal orders-
dc.subjectHalf-integer weight modular forms-
dc.subjectKohnen's plus space-
dc.subjectShimura lifts-
dc.titleRepresentations of integers by ternary quadratic formsen_US
dc.typeArticleen_US
dc.description.naturepostprint-
dc.identifier.doi10.1142/S1793042110002831en_US
dc.identifier.scopuseid_2-s2.0-77951602527en_US
dc.identifier.volume6en_US
dc.identifier.issue1en_US
dc.identifier.spage127en_US
dc.identifier.epage158en_US
dc.identifier.isiWOS:000275714000009-

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