On the Proportion of Quadratic Twists for Non-vanishing and Vanishing Central Values of L-Functions Attached to Primitive Forms

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


Let \(S_{2k}^{\mathrm{new}}(\Gamma _{0}(N))\) be the space of newforms of weight 2k on \(\Gamma _{0}(N)\). Let k and N be positive integers and \(f \in S_{2k}^{\mathrm{new}}(\Gamma _{0}(N))\) a primitive form. Let r be either 0 or 1.


Primitive Form Newform Half-integral Weight Cusp Forms Shimura Correspondence Semistable Elliptic Curve 
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The author is very grateful to Professor Atsushi Yamagami for variable guidance and kind help. He is also grateful to Professor Atsushi Murase and Professor Bernhard Heim for valuable comments on improving the manuscript and supports for my participation in the international workshop on mathematics held at Oman in February 2012.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of MathematicsKyoto Sangyo UniversityKyotoJapan

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