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FOURIER COEFFICIENTS OF GENERALIZED MODULAR FORMS OF NEGATIVE WEIGHT

WISSAM RAJI

Department of Mathematics, American University of Beirut, Beirut, Lebanon

https://doi.org/10.1142/S1793042109002006Cited by:7 (Source: Crossref)

Abstract

The Fourier coefficients of classical modular forms of negative weights have been determined for the case for which F(τ) belongs to a subgroup of the full modular group [9]. In this paper, we determine the Fourier coefficients of generalized modular forms of negative weights using the circle method.

Keywords:

AMSC: 11F11, 11F75

References

F. Diamond and J. Shurmann , A First Course in Modular Forms ( Springer-Verlag , Berlin-Heidelberg-New York , 2005 ) . Google Scholar
M. Eichler, Acta Arith. 11, 169 (1965). Crossref, Google Scholar
M. Knopp and G. Mason, J. Number Theory 99, 1 (2003), DOI: 10.1016/S0022-314X(02)00065-3. Crossref, Web of Science, Google Scholar
M. Knopp and G. Mason, Acta Arith. 110(2), 117 (2003), DOI: 10.4064/aa110-2-2. Crossref, Web of Science, Google Scholar
J. Lehner, Michigan Math. J. 4, 265 (1957). Google Scholar
J. Lehner, Michigan Math. J. 6, 173 (1959). Google Scholar
H. Rademacher and H. Zuckerman, Ann. of Math. (2) 39(2), 433 (1938), DOI: 10.2307/1968796. Crossref, Google Scholar
W. Raji, Eichler cohomology theorem for generalized modular forms, submitted for publication . Google Scholar
H. Zuckerman, Trans. Amer. Math. Soc. 45, 298 (1939), DOI: 10.2307/1990119. Crossref, Web of Science, Google Scholar