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On vector spaces of certain modular forms of given weights

Published online by Cambridge University Press:  17 April 2009

A.R. Aggarwal  and
M.K. Agrawal
A.R. Aggarwal
Affiliation:
Department of Mathematics, Panjab University, Chandigarh, India, and I.B. College, Panipat, India
M.K. Agrawal
Affiliation:
Department of Mathematics, Panjab University, Chandigarh, India.
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 16 , Issue 3 , June 1977 , pp. 371 - 378
Copyright
Copyright © Australian Mathematical Society 1977

References

[1]Serre, Jean-Pierre, “Formes modulaires et fonctions zêta p–adiques”, Modular functions of one variable III, 191–268 (Proc. Internat. Summer School, University of Antwerp, RUCA, 1972. Lecture Notes in Mathematics, 350. Springer-Verlag, Berlin, Heidelberg, New York, 1973).CrossRefGoogle Scholar