Congruences of two-variable p-adic L-functions of congruent modular forms of different weights

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Vatsal (Duke Math J 98(2):397-419, 1999) proved that there are congruences between the p-adic L-functions (constructed by Mazur and Swinnerton-Dyer in Invent Math 25:1-61, 1974) of congruent modular forms of the same weight under some conditions. On the other hand, Kim (J Number Theory 144: 188-218, 2014), the second author, constructed two-variable p-adic L-functions of modular forms attached to imaginary quadratic fields generalizing Hida's work (Invent Math 79:159-195, 1985), and the novelty of his construction was that it works whether p is an ordinary prime or not. In this paper, we prove congruences between the two-variable p-adic L-functions (of the second author) of congruent modular forms of different but congruent weights under some conditions when p is a nonordinary prime for the modular forms. This result generalizes the work of Emerton et al. (Invent Math 163(3): 523-580, 2006), who proved similar congruences between the p-adic L-functions of congruent modular forms of congruent weights when p is an ordinary prime.
Publisher
SPRINGER
Issue Date
2017-05
Language
English
Article Type
Article
Keywords

IWASAWA INVARIANTS; INTERPOLATION; CURVES

Citation

RAMANUJAN JOURNAL, v.43, no.1, pp.163 - 195

ISSN
1382-4090
DOI
10.1007/s11139-016-9819-8
URI
http://hdl.handle.net/10203/223653
Appears in Collection
MA-Journal Papers(저널논문)
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