Keywords: modular form; harmonic Maass Jacobi form; holomorphic projection; Hurwitz class number
@article{10_21136_CMJ_2020_0427_19,
author = {Xiong, Ran and Zhou, Haigang},
title = {Constructing modular forms from harmonic {Maass} {Jacobi} forms},
journal = {Czechoslovak Mathematical Journal},
pages = {455--473},
year = {2021},
volume = {71},
number = {2},
doi = {10.21136/CMJ.2020.0427-19},
mrnumber = {4263180},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0427-19/}
}
TY - JOUR AU - Xiong, Ran AU - Zhou, Haigang TI - Constructing modular forms from harmonic Maass Jacobi forms JO - Czechoslovak Mathematical Journal PY - 2021 SP - 455 EP - 473 VL - 71 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0427-19/ DO - 10.21136/CMJ.2020.0427-19 LA - en ID - 10_21136_CMJ_2020_0427_19 ER -
%0 Journal Article %A Xiong, Ran %A Zhou, Haigang %T Constructing modular forms from harmonic Maass Jacobi forms %J Czechoslovak Mathematical Journal %D 2021 %P 455-473 %V 71 %N 2 %U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0427-19/ %R 10.21136/CMJ.2020.0427-19 %G en %F 10_21136_CMJ_2020_0427_19
Xiong, Ran; Zhou, Haigang. Constructing modular forms from harmonic Maass Jacobi forms. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 2, pp. 455-473. doi: 10.21136/CMJ.2020.0427-19
[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). | DOI | MR | JFM
[2] Bringmann, K., Richter, O. K.: Zagier-type dualities and lifting maps for harmonic Maass-Jacobi forms. Adv. Math. 225 (2010), 2298-2315. | DOI | MR | JFM
[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. | DOI | MR | JFM
[4] Cohen, H.: Sums involving the values at negative integers of $L$-functions of quadratic characters. Math. Ann. 217 (1975), 271-285. | DOI | MR | JFM
[5] Eichler, M., Zagier, D.: The Theory of Jacobi Forms. Progress in Mathematics 55. Birkhäuser, Boston (1985). | DOI | MR | JFM
[6] Gross, B. H., Zagier, D.: Heegner points and derivatives of $L$-series. Invent. Math. 84 (1986), 225-320. | DOI | MR | JFM
[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. | DOI | MR | JFM
[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
[9] Mertens, M. H.: Eichler-Selberg type identities for mixed mock modular forms. Adv. Math. 301 (2016), 359-382. | DOI | MR | JFM
[10] Sturm, J.: Projections of ${{\mathbb C}}^{\infty}$ automorphic forms. Bull. Am. Math. Soc., New Ser. 2 (1980), 435-439. | DOI | MR | JFM
Cité par Sources :