Abstract
We extend the heuristic introduced by Conrey, Farmer, Keating, Rubinstein, and Snaith in order to formulate conjectures for the -moments of L-functions of elliptic curves twisted by cubic characters. We also apply the work of Keating and Snaith on the -moments of characteristic polynomials of unitary matrices to extend our conjecture to such that and . Our conjectures are then numerically tested for two families. A novelty of our conjectures is that cubic twists naturally lead us to consider the possibility .
2010 Mathematics Subject Classification:
Correction Statement
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Acknowledgments
The authors thank to Hershy Kisilevsky for many useful discussions, Andrew Granville for suggesting the formula of Lemma 2.2 to show that is an integer, Jon Keating and Michael Rubinstein for bringing our attention to the status of the computations of coefficients for zeta functions and quadratic twists, Pablo Bianucci for helpful advice in some of the numerical computations, and the anonymous referee for helpful corrections and suggestions. The authors are very grateful to the Centre de Recherches Mathématiques (CRM) for the access to their cluster and to Jack Fearnley for providing his L-value data.
Declaration of Interest
No potential conflict of interest was reported by the author(s).