A formula for the central values of twisted $L$-functions derived from the Shimura correspondence
Volume 194 / 2020
Acta Arithmetica 194 (2020), 155-178
MSC: Primary 11F67; Secondary 11F11, 11F37.
DOI: 10.4064/aa190110-12-8
Published online: 2 March 2020
Abstract
There is a well established connection between half-integral weight modular forms and integral weight modular forms. By combining two identities relating the Fourier coefficients of half-integral weight forms and integral weight forms we establish an asymptotic formula for the weighted mean of integral weight modular forms at the central point.
