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Keywords:
modular form; harmonic Maass Jacobi form; holomorphic projection; Hurwitz class number
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).
References:
[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 10.1090/coll/064 | MR 3729259 | Zbl 06828732
[2] Bringmann, K., Richter, O. K.: Zagier-type dualities and lifting maps for harmonic Maass-Jacobi forms. Adv. Math. 225 (2010), 2298-2315. DOI 10.1016/j.aim.2010.03.033 | MR 2680205 | Zbl 1264.11039
[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 10.1007/BF02677465 | MR 1464364 | Zbl 0890.11017
[4] Cohen, H.: Sums involving the values at negative integers of $L$-functions of quadratic characters. Math. Ann. 217 (1975), 271-285. DOI 10.1007/BF01436180 | MR 0382192 | Zbl 0311.10030
[5] Eichler, M., Zagier, D.: The Theory of Jacobi Forms. Progress in Mathematics 55. Birkhäuser, Boston (1985). DOI 10.1007/978-1-4684-9162-3 | MR 0781735 | Zbl 0554.10018
[6] Gross, B. H., Zagier, D.: Heegner points and derivatives of $L$-series. Invent. Math. 84 (1986), 225-320. DOI 10.1007/BF01388809 | MR 0833192 | Zbl 0608.14019
[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 10.1073/pnas.1311621111 | MR 3200180 | Zbl 1355.11039
[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
[9] Mertens, M. H.: Eichler-Selberg type identities for mixed mock modular forms. Adv. Math. 301 (2016), 359-382. DOI 10.1016/j.aim.2016.06.016 | MR 3539378 | Zbl 1404.11054
[10] Sturm, J.: Projections of ${{\mathbb C}}^{\infty}$ automorphic forms. Bull. Am. Math. Soc., New Ser. 2 (1980), 435-439. DOI 10.1090/S0273-0979-1980-14757-6 | MR 561527 | Zbl 0433.10013
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