On the vanishing of twists of L-functions of elliptic curves Chantal ...

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$MATH 208 - Department of Mathematics and Statistics - Concordia ...$

$MATH 252 - Department of Mathematics and Statistics$

$Mast 330 /Math 370 Midterm Test 27 October 2004$

$MATH 208 - Department of Mathematics and Statistics - Concordia ...$

$Mast 330 / Math 370 Sec A Final Exam December 2002$

Lower bounds and asymptotic for N ∗ (X)N ≥2 (X) ≫ X 1/2 (Gouvêa-Mazur)under the parity conjectureN ≥2 (X) ≫ X 1/7 log −2 (X) (Stewart-Top)N ≥2 (X) ≫ X 1/3 (Rubin-Silverberg)when E has rational 2-torsionN ≥3 (X) ≫ X 1/6 (Rubin-Silverberg)for some special EConjecture (Conrey, Keating, Rubinstein andSnaith) There are constants b E ≠ 0 and e Esuch thatwhen X → ∞.N ≥2,even (X) ∼ b E X 3/4 log e E X3
Higher order twistsLet k be an integer greater than 2, and considercharacters of order k.Questions:Infinitely many χ with L E (1, χ) = 0 ?Positive proportion of χ with L E (1, χ) = 0 ?Precise asymptotic ?Empirical vanishing for cubic twistsCurve Maximal Number of Number of(Torsion) conductor characters vanishingE11A (5) 2,023,513 320,795 1152E14A (6) 2,108,767 260,001 4347E15A (8) 399,979 51,890 807E32A (4) 300,217 47,577 117E36A (6) 283,051 36,718 346E37A (1) 279,211 41,991 559E37B (3) 364,723 54,830 1899E389A (1) 99,991 15,851 4084
Page 1 and 2: On the vanishing of twists of L-fun
Page 3: Quadratic charactersLet χ d be a q
Page 7 and 8: Random matricesPhilosophy for a fam
Page 9: MomentsLet k be a positive integer.
Page 12 and 13: Random matricesKeating and Snaith:
Page 14 and 15: When N → ∞R(N) → N 1/4 G 2 (1
Page 16 and 17: Distribution of the integers n χCu
Page 18: Empirical results for E11A and E14A

On the vanishing of twists of L-functions of elliptic curves Chantal ...

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