Geodesic
An Elementary Proof of a Weak Exceptional Zero Conjecture
Canadian journal of mathematics, Tome 56 (2004) no. 2, pp. 373-405

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we extend Darmon's theory of “integration on ${{\text{H}}_{p}}\times \text{H}$ ” to cusp forms $f$ of higher even weight. This enables us to prove a “weak exceptional zero conjecture”: that when the $p$ -adic $L$ -function of $f$ has an exceptional zero at the central point, the $\mathcal{L}$ -invariant arising is independent of a twist by certain Dirichlet characters.
DOI : 10.4153/CJM-2004-018-4
Mots-clés : 11F11, 11F67 
Orton, Louisa. An Elementary Proof of a Weak Exceptional Zero Conjecture. Canadian journal of mathematics, Tome 56 (2004) no. 2, pp. 373-405. doi: 10.4153/CJM-2004-018-4
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[Col] Colmez, P., Théorie d'Iwasawa des Répresentations de de Rham d'un corps local. Ann. of Math. 148(1998), 485–571. Google Scholar

[Cr] Cremona, J. E., Algorithms for modular elliptic curves. CUP, (1992). Google Scholar

[Dar] Darmon, H., Integration on ℋ × ℋ and arithmetic applications. Ann. of Math. 154(2001), 589–639. Google Scholar

[GS] Greenberg, R. and Stevens, G., p-adic L-functions and p-adic periods of modular forms. Invent. Math. 111(1993), 401–447. Google Scholar

[Hi] Hida, H., Elementary theory of L-functions and Eisenstein series. London Mathematical Society Student Texts (1993). Google Scholar

[Kit] Kitagawa, K., On Standard p-adic L-functions of families of elliptic cusp forms. In: p-adic Monodromy and the Birch and Swinnerton-Dyer Conjecture, Amer.Math. Soc., (1991). Google Scholar

[Mil] Mildenhall, S., Cycles in a product of elliptic curves and a group analogous to the class group. Duke Math J. (2) 67(1992), 387–406. Google Scholar

[Miy] Miyake, T., Modular Forms. Springer-Verlag, 1976. Google Scholar

[MTT] Mazur, B., Tate, J., Teitelbaum, J., On p-adic analogues of the conjectures of Birch and Swinnerton-Dyer. Invent. Math. 84(1986), 1–48. Google Scholar

[Ro] Rohrlich, D. E., Nonvanishing of L-functions and structure of Mordell-Weil groups. J. Reine Angew. Math 417(1991), 1–26. Google Scholar

[Ser] Serre, J-P., Trees. Springer-Verlag, 1980. Google Scholar

[Tei] Teitelbaum, J., Values of p-adic L-functions and a p-adic Poisson Kernel. Invent. Math. 101(1990), 395–410. Google Scholar

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