# 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} }

- Published 2004 in Experimental Mathematics
DOI:10.1080/10586458.2004.10504532

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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