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On the Special Values of Certain L-Series Related to Half-Integral Weight Modular Forms

  • Hidenori KatsuradaEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 115)

Abstract

Let h be a cuspidal Hecke eigenform of half-integral weight, and \(E_{n/2+1/2}\) be Cohen’s Eisenstein series of weight \(n/2 + 1/2.\) For a Dirichlet character χ we define a certain linear combination \(R^{(\chi )}(s,h,E_{n/+1/2})\) of the Rankin–Selberg convolution products of h and \(E_{n/2+1/2}\) twisted by Dirichlet characters related with χ. We then prove a certain algebraicity result for \(R^{(\chi )}(l,h,E_{n/2+1/2})\) with l integers.

Mathematics Subject Classification (2000)

Primary 11F67 11F46 11F66 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Muroran Institute of TechnologyMuroranJapan

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