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A formula for the central values of twisted $L$-functions derived from the Shimura correspondence

Volume 194 / 2020

Sam Fotis 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.

Authors

  • Sam FotisMath. Department
    Columbus State Community College
    550 E Spring St.
    Columbus, OH 43215, U.S.A.
    e-mail

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