Wen-Ching Winnie Li, Ling Long, Fang-Ting Tu, “Computing Special $L$-Values of Certain Modular Forms with Complex Multiplication”, SIGMA, 2018, том 14,090, 32 стр.

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

Аннотация: 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 $\mathbb{Q}$.

Ключевые слова: $L$-values; modular forms; complex multiplications; hypergeometric functions; Eisenstein series.

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

Поступила: 3 апреля 2018 г.; в окончательном варианте 18 августа 2018 г.; опубликована 29 августа 2018 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2018.090