On vector spaces of certain modular forms of given weights
1977 ◽
Vol 16
(3)
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pp. 371-378
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Keyword(s):
Let p be a rational prime and Qp be the field of p–adic numbers. Jean-Pierre Serre [Lecture Notes in Mathematics, 350, 191–268 (1973)] had defined p–adic modular forms as the limits of sequences of modular forms over the modular group SL2(Z). He proved that with each non-zero p–adic modular form there is associated a unique element called its weight k. The p–adic modular forms having the same weight form a Qp–vector space.The object of this paper is to obtain a basis of p–adic modular forms and thus to know precisely all p–adic modular forms of a given weight k. The dimension of such modular forms as a Qp–vector space is countably infinite.
2009 ◽
Vol 05
(05)
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pp. 845-857
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Keyword(s):
1974 ◽
Vol 18
(3)
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pp. 376-384
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Keyword(s):
1979 ◽
Vol 86
(3)
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pp. 461-466
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Keyword(s):
1954 ◽
Vol 50
(2)
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pp. 305-308
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Keyword(s):
Keyword(s):
2014 ◽
Vol 57
(3)
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pp. 485-494
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Keyword(s):
Keyword(s):
2010 ◽
Vol 06
(01)
◽
pp. 69-87
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