File Download
There are no files associated with this item.
Links for fulltext
(May Require Subscription)
- Publisher Website: 10.1016/j.jnt.2011.12.011
- Scopus: eid_2-s2.0-84863421506
- WOS: WOS:000301324400001
- Find via
Supplementary
- Citations:
- Appears in Collections:
Article: On a variance of Hecke eigenvalues in arithmetic progressions
| Title | On a variance of Hecke eigenvalues in arithmetic progressions | ||||
|---|---|---|---|---|---|
| Authors | |||||
| Keywords | Divisor function Fourier coefficient Hecke eigenvalue Holomorphic cusp form Variance | ||||
| Issue Date | 2012 | ||||
| Publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/jnt | ||||
| Citation | Journal of Number Theory, 2012, v. 132 n. 5, p. 869-887 How to Cite? | ||||
| Abstract | Let a(n) be the eigenvalue of a holomorphic Hecke eigenform f under the nth Hecke operator. We derive asymptotic formulae for the variance ∑ b=1 q|∑ n≤Xn≡ b(modq)a(n)| 2 when X 1/4+ε≤q≤X 1/2-ε or X 1/2+ε≤q≤X 1-ε, that exhibit distinct behavior. The analogous problem for the divisor function will be studied as well. © 2012 Elsevier Inc. | ||||
| Persistent Identifier | http://hdl.handle.net/10722/156279 | ||||
| ISSN | 2023 Impact Factor: 0.6 2023 SCImago Journal Rankings: 0.780 | ||||
| ISI Accession Number ID |
Funding Information: The authors wish to thank the referees for their readings, the explanatory viewpoint in Remark 3 and criticism. Lau is supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (HKU702308P). | ||||
| References |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Lau, YK | en_US |
| dc.contributor.author | Zhao, L | en_US |
| dc.date.accessioned | 2012-08-08T08:41:09Z | - |
| dc.date.available | 2012-08-08T08:41:09Z | - |
| dc.date.issued | 2012 | en_US |
| dc.identifier.citation | Journal of Number Theory, 2012, v. 132 n. 5, p. 869-887 | en_US |
| dc.identifier.issn | 0022-314X | en_US |
| dc.identifier.uri | http://hdl.handle.net/10722/156279 | - |
| dc.description.abstract | Let a(n) be the eigenvalue of a holomorphic Hecke eigenform f under the nth Hecke operator. We derive asymptotic formulae for the variance ∑ b=1 q|∑ n≤Xn≡ b(modq)a(n)| 2 when X 1/4+ε≤q≤X 1/2-ε or X 1/2+ε≤q≤X 1-ε, that exhibit distinct behavior. The analogous problem for the divisor function will be studied as well. © 2012 Elsevier Inc. | en_US |
| dc.language | eng | en_US |
| dc.publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/jnt | en_US |
| dc.relation.ispartof | Journal of Number Theory | en_US |
| dc.subject | Divisor function | en_US |
| dc.subject | Fourier coefficient | en_US |
| dc.subject | Hecke eigenvalue | en_US |
| dc.subject | Holomorphic cusp form | en_US |
| dc.subject | Variance | en_US |
| dc.title | On a variance of Hecke eigenvalues in arithmetic progressions | en_US |
| dc.type | Article | en_US |
| dc.identifier.email | Lau, YK: yklau@maths.hku.hk | en_US |
| dc.identifier.email | Zhao, L: zhaolilu@gmail.com | - |
| dc.identifier.authority | Lau, YK=rp00722 | en_US |
| dc.description.nature | link_to_subscribed_fulltext | en_US |
| dc.identifier.doi | 10.1016/j.jnt.2011.12.011 | en_US |
| dc.identifier.scopus | eid_2-s2.0-84863421506 | en_US |
| dc.identifier.hkuros | 206537 | - |
| dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-84856439849&selection=ref&src=s&origin=recordpage | en_US |
| dc.identifier.volume | 132 | en_US |
| dc.identifier.issue | 5 | en_US |
| dc.identifier.spage | 869 | en_US |
| dc.identifier.epage | 887 | en_US |
| dc.identifier.isi | WOS:000301324400001 | - |
| dc.publisher.place | United States | en_US |
| dc.identifier.scopusauthorid | Zhao, L=54942149800 | en_US |
| dc.identifier.scopusauthorid | Lau, YK=35724053400 | en_US |
| dc.identifier.citeulike | 10326545 | - |
| dc.identifier.issnl | 0022-314X | - |