On the Vanishing of Twisted L-Functions of Elliptic Curves

@article{David2004OnTV,
  title={On the Vanishing of Twisted L-Functions of Elliptic Curves},
  author={Chantal David and Jack Fearnley and Hershy Kisilevsky},
  journal={Experimental Mathematics},
  year={2004},
  volume={13},
  pages={185-198}
}
Let E be an elliptic curve over Q with L-function LE(s). We use the random matrix model of Katz and Sarnak to develop a heuristic for the frequency of vanishing of the twisted L-functions LE(1, χ), as χ runs over the Dirichlet characters of order 3 (cubic twists). The heuristic suggests that the number of cubic twists of conductor less than X for which LE(1, χ) vanishes is asymptotic to bEX 1/2 logE X for some constants bE , eE depending only on E. We also compute explicitely the conjecture of… CONTINUE READING
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