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
DOI:
https://doi.org/10.1090/S0894-0347-2010-00680-7
Published electronically:
September 8, 2010
MathSciNet review:
2726599
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We make finiteness conjectures on the composite of Hecke fields of classical members of a -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
-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
Email:
hida@math.ucla.edu
DOI:
https://doi.org/10.1090/S0894-0347-2010-00680-7
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.
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American Mathematical Society