| Title:
|
Constructing modular forms from harmonic Maass Jacobi forms (English) |
| Author:
|
Xiong, Ran |
| Author:
|
Zhou, Haigang |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
71 |
| Issue:
|
2 |
| Year:
|
2021 |
| Pages:
|
455-473 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We construct a family of modular forms from harmonic Maass Jacobi forms by considering their Taylor expansion and using the method of holomorphic projection. As an application we present a certain type Hurwitz class relations which can be viewed as a generalization of Mertens' result in M. H. Mertens (2016). (English) |
| Keyword:
|
modular form |
| Keyword:
|
harmonic Maass Jacobi form |
| Keyword:
|
holomorphic projection |
| Keyword:
|
Hurwitz class number |
| MSC:
|
11F30 |
| MSC:
|
11F37 |
| MSC:
|
11F50 |
| idZBL:
|
07361079 |
| idMR:
|
MR4263180 |
| DOI:
|
10.21136/CMJ.2020.0427-19 |
| . |
| Date available:
|
2021-05-20T13:43:43Z |
| Last updated:
|
2023-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148915 |
| . |
| Reference:
|
[1] Bringmann, K., Folsom, A., Ono, K., Rolen, L.: Harmonic Maass Forms and Mock Modular Forms: Theory and Applications.American Mathematical Society Colloquium Publications 64. American Mathematical Society, Providence (2017). Zbl 06828732, MR 3729259, 10.1090/coll/064 |
| Reference:
|
[2] Bringmann, K., Richter, O. K.: Zagier-type dualities and lifting maps for harmonic Maass-Jacobi forms.Adv. Math. 225 (2010), 2298-2315. Zbl 1264.11039, MR 2680205, 10.1016/j.aim.2010.03.033 |
| Reference:
|
[3] Choie, Y.: Correspondence among Eisenstein series $E_{2,1}(\tau,z)$, $H_{\frac{3}{2}}(\tau)$ and $E_{2}(\tau)$.Manuscr. Math. 93 (1997), 177-187. Zbl 0890.11017, MR 1464364, 10.1007/BF02677465 |
| Reference:
|
[4] Cohen, H.: Sums involving the values at negative integers of $L$-functions of quadratic characters.Math. Ann. 217 (1975), 271-285. Zbl 0311.10030, MR 0382192, 10.1007/BF01436180 |
| Reference:
|
[5] Eichler, M., Zagier, D.: The Theory of Jacobi Forms.Progress in Mathematics 55. Birkhäuser, Boston (1985). Zbl 0554.10018, MR 0781735, 10.1007/978-1-4684-9162-3 |
| Reference:
|
[6] Gross, B. H., Zagier, D.: Heegner points and derivatives of $L$-series.Invent. Math. 84 (1986), 225-320. Zbl 0608.14019, MR 0833192, 10.1007/BF01388809 |
| Reference:
|
[7] Imamoğlu, Ö., Raum, M., Richter, O. K.: Holomorphic projections and Ramanujan's mock theta functions.Proc. Natl. Acad. Sci. USA 111 (2014), 3961-3967. Zbl 1355.11039, MR 3200180, 10.1073/pnas.1311621111 |
| Reference:
|
[8] Mertens, M. H.: Mock Modular Forms and Class Numbers of Quadratic Forms: PhD Thesis.Universität zu Köln, Köln (2014), Available at \let \relax\brokenlink{http://kups.ub.uni-koeln.de/id/{eprint/5686}}. MR 3377995 |
| Reference:
|
[9] Mertens, M. H.: Eichler-Selberg type identities for mixed mock modular forms.Adv. Math. 301 (2016), 359-382. Zbl 1404.11054, MR 3539378, 10.1016/j.aim.2016.06.016 |
| Reference:
|
[10] Sturm, J.: Projections of ${{\mathbb C}}^{\infty}$ automorphic forms.Bull. Am. Math. Soc., New Ser. 2 (1980), 435-439. Zbl 0433.10013, MR 561527, 10.1090/S0273-0979-1980-14757-6 |
| . |
