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Hecke fields of analytic families of modular forms

Author: Haruzo Hida
Journal: J. Amer. Math. Soc. 24 (2011), 51-80
MSC (2010): Primary 11E16, 11F11, 11F25, 11F27, 11F30, 11F33, 11F80
Published electronically: September 8, 2010
MathSciNet review: 2726599
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Abstract: We make finiteness conjectures on the composite of Hecke fields of classical members of a $ p$-adic analytic family of slope 0 elliptic modular forms in the vertical case (with fixed level varying weight). In the horizontal case (fixed weight varying $ p$-power level), we prove the corresponding statements.

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Additional Information

Haruzo Hida
Affiliation: Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095-1555

Received by editor(s): June 19, 2009
Received by editor(s) in revised form: February 8, 2010, and April 29, 2010
Published electronically: September 8, 2010
Additional Notes: The author is partially supported by the NSF grant: DMS 0753991 and DMS 0854949, and part of this work was done during the author’s stay in January to March 2010 at the Institut Henri Poincaré - Centre Emile Borel. The author thanks this institution for its hospitality and support.
Article copyright: © Copyright 2010 American Mathematical Society