Number Theory
A counterexample to the Gouvêa–Mazur conjecture
Comptes Rendus. Mathématique, Volume 338 (2004) no. 10, pp. 751-753.

Gouvêa and Mazur made a precise conjecture about slopes of modular forms. Weaker versions of this conjecture were established by Coleman and Wan. In this Note, we exhibit examples contradicting the full conjecture as it currently stands.

Gouvêa et Mazur ont proposé une conjecture précise au sujet des pentes des formes modulaires. Des versions plus faibles de cette conjecture ont été prouvées par Coleman et Wan. Dans cette Note, nous exhibons des exemples contredisant la conjecture.

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DOI: 10.1016/j.crma.2004.03.016
Buzzard, Kevin 1; Calegari, Frank 2

1 Department of Mathematics, Imperial College, 180, Queen's Gate, London SW7 2AZ, UK
2 1, Science Center, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
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Buzzard, Kevin; Calegari, Frank. A counterexample to the Gouvêa–Mazur conjecture. Comptes Rendus. Mathématique, Volume 338 (2004) no. 10, pp. 751-753. doi : 10.1016/j.crma.2004.03.016. http://www.numdam.org/articles/10.1016/j.crma.2004.03.016/

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