Wen-Ching Winnie Li, Ling Long, Fang-Ting Tu, “Computing Special <nobr>$L$</nobr>-Values of Certain Modular Forms with Complex Multiplication”, SIGMA, 2018, Volume 14,090, 32 pp.

Computing Special $L$-Values of Certain Modular Forms with Complex Multiplication

Wen-Ching Winnie Li^a, Ling Long^b, Fang-Ting Tu^b

^a Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA
^b Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA

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.

MSC: 11F11; 11F67; 11M36; 33C05

Received: April 3, 2018; in final form August 18, 2018; Published online August 29, 2018

Language: English

DOI: 10.3842/SIGMA.2018.090