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Acknowledgement to Reviewers of Mathematics in 2015
Article

Modular Forms and Weierstrass Mock Modular Forms

Department of Mathematics, Emory University, Emory, Atlanta, GA 30322, USA
Academic Editor: Alexander Berkovich
Mathematics 2016, 4(1), 5; https://doi.org/10.3390/math4010005
Received: 12 November 2015 / Revised: 12 January 2016 / Accepted: 19 January 2016 / Published: 2 February 2016
Alfes, Griffin, Ono, and Rolen have shown that the harmonic Maass forms arising from Weierstrass ζ-functions associated to modular elliptic curves “encode” the vanishing and nonvanishing for central values and derivatives of twisted Hasse-Weil L-functions for elliptic curves. Previously, Martin and Ono proved that there are exactly five weight 2 newforms with complex multiplication that are eta-quotients. In this paper, we construct a canonical harmonic Maass form for these five curves with complex multiplication. The holomorphic part of this harmonic Maass form arises from the Weierstrass ζ-function and is referred to as the Weierstrass mock modular form. We prove that the Weierstrass mock modular form for these five curves is itself an eta-quotient or a twist of one. Using this construction, we also obtain p-adic formulas for the corresponding weight 2 newform using Atkin’s U-operator. View Full-Text
Keywords: modular forms; weierstrass mock modular forms; eta-quotients modular forms; weierstrass mock modular forms; eta-quotients
MDPI and ACS Style

Clemm, A. Modular Forms and Weierstrass Mock Modular Forms. Mathematics 2016, 4, 5. https://doi.org/10.3390/math4010005

AMA Style

Clemm A. Modular Forms and Weierstrass Mock Modular Forms. Mathematics. 2016; 4(1):5. https://doi.org/10.3390/math4010005

Chicago/Turabian Style

Clemm, Amanda. 2016. "Modular Forms and Weierstrass Mock Modular Forms" Mathematics 4, no. 1: 5. https://doi.org/10.3390/math4010005

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