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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Analytic continuation of overconvergent eigenforms
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by Kevin Buzzard PDF
J. Amer. Math. Soc. 16 (2003), 29-55 Request permission


Let $f$ be an overconvergent $p$-adic eigenform of level $Np^r$, $r\geq 1$, with non-zero $U_p$-eigenvalue. We show how $f$ may be analytically continued to a subset of $X_1(Np^r)^{\mathrm {an}}$ containing, for example, all the supersingular locus. Using these results we extend the main theorem of our earlier work with R. Taylor to many ramified cases.
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Additional Information
  • Kevin Buzzard
  • Affiliation: Department of Mathematics, Imperial College, Huxley Building, 180 Queen’s Gate, London SW7 2B2, England
  • MR Author ID: 363443
  • ORCID: 0000-0002-7187-5109
  • Email:
  • Received by editor(s): September 24, 2001
  • Published electronically: September 19, 2002
  • Additional Notes: The author would like to thank the Miller Institute and UC Berkeley for the financial support and hospitality they offered him whilst he was obtaining the majority of these results. The write-up was done over a period of several years, in Rennes, the IHP in Paris, Cambridge UK, and Imperial College London, and the author would also like to thank these institutions for their hospitality. He would also like to thank the referee for several helpful remarks
  • © Copyright 2002 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 16 (2003), 29-55
  • MSC (2000): Primary 11F80, 11F33; Secondary 11G18, 14G22, 14G35
  • DOI:
  • MathSciNet review: 1937198