Links for fulltext
(May Require Subscription)
- Publisher Website: 10.1142/S1793042110002831
- Scopus: eid_2-s2.0-77951602527
- WOS: WOS:000275714000009
- Find via
Supplementary
- Citations:
- Appears in Collections:
Article: Representations of integers by ternary quadratic forms
Title | Representations of integers by ternary quadratic forms |
---|---|
Authors | |
Keywords | Quaternion algebra Elliptic curves Maximal orders Half-integer weight modular forms Kohnen's plus space Shimura lifts |
Issue Date | 2010 |
Citation | International Journal of Number Theory, 2010, v. 6 n. 1, p. 127-158 How to Cite? |
Abstract | We 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 Identifier | http://hdl.handle.net/10722/192191 |
ISSN | 2023 Impact Factor: 0.5 2023 SCImago Journal Rankings: 0.549 |
ISI Accession Number ID |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Kane, B | en_US |
dc.date.accessioned | 2013-10-23T09:27:17Z | - |
dc.date.available | 2013-10-23T09:27:17Z | - |
dc.date.issued | 2010 | en_US |
dc.identifier.citation | International Journal of Number Theory, 2010, v. 6 n. 1, p. 127-158 | en_US |
dc.identifier.issn | 1793-0421 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/192191 | - |
dc.description.abstract | We 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.language | eng | en_US |
dc.relation.ispartof | International Journal of Number Theory | en_US |
dc.subject | Quaternion algebra | - |
dc.subject | Elliptic curves | - |
dc.subject | Maximal orders | - |
dc.subject | Half-integer weight modular forms | - |
dc.subject | Kohnen's plus space | - |
dc.subject | Shimura lifts | - |
dc.title | Representations of integers by ternary quadratic forms | en_US |
dc.type | Article | en_US |
dc.description.nature | postprint | - |
dc.identifier.doi | 10.1142/S1793042110002831 | en_US |
dc.identifier.scopus | eid_2-s2.0-77951602527 | en_US |
dc.identifier.volume | 6 | en_US |
dc.identifier.issue | 1 | en_US |
dc.identifier.spage | 127 | en_US |
dc.identifier.epage | 158 | en_US |
dc.identifier.isi | WOS:000275714000009 | - |
dc.identifier.issnl | 1793-7310 | - |