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Symmetry, Integrability and Geometry: Methods and Applications, 2018, Volume 14, 090, 32 pp.
DOI: https://doi.org/10.3842/SIGMA.2018.090 (Mi sigma1389) 		 
Computing Special $L$-Values of Certain Modular Forms with Complex Multiplication

Wen-Ching Winnie Lia, Ling Longb, Fang-Ting Tub

a Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA
b Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA
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DOI: https://doi.org/10.3842/SIGMA.2018.090
Abstract: In this expository paper, we illustrate two explicit methods which lead to special $L$-values of certain modular forms admitting complex multiplication (CM), motivated in part by properties of $L$-functions obtained from Calabi–Yau manifolds defined over $\mathbb{Q}$.
Keywords: $L$-values; modular forms; complex multiplications; hypergeometric functions; Eisenstein series.
Funding agency Grant number
Simons Foundation 355798
National Science Foundation DMS #1602047
Received: April 3, 2018; in final form August 18, 2018; Published online August 29, 2018
Bibliographic databases:
Document Type: Article
MSC: 11F11; 11F67; 11M36; 33C05
Language: English
Citation: Wen-Ching Winnie Li, Ling Long, Fang-Ting Tu, “Computing Special $L$-Values of Certain Modular Forms with Complex Multiplication”, SIGMA, 14 (2018), 090, 32 pp.
Citation in format AMSBIB
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\by Wen-Ching Winnie~Li, Ling~Long, Fang-Ting~Tu
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