None

Philippe Michel, Jeffrey M. VanderKam, Philippe Michel

Type: Article

Publication Date: 2002-01-01

Citations: 17

DOI: https://doi.org/10.1023/a:1020544429383

Abstract

Given three distinct primitive complex characters χ1,χ2,χ3 satisfying some technical conditions, we prove that the triple product of twisted L-functions L(f·χ1,1/2) L(f·χ2,1/2) L(f·χ3,1/2) does not vanish for a positive proportion of weight 2 primitive forms for Γ0(q), when q goes to infinity through the set of prime numbers. This result, together with some variants, implies the existence of quotients of J0(q) of large dimension satisfying the Birch–Swinnerton-Dyer conjecture over cyclic number fields of degree less than 5.

Locations

Infoscience (Ecole Polytechnique Fédérale de Lausanne) - View - PDF
Compositio Mathematica - View - PDF

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+	On cusp forms for co-finite subgroups ofPSL(2,?)	1985	Ralph S. Phillips Peter Sarnak
+	Newforms and functional equations	1975	Wen Ch ing Winnie Li