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http://dx.doi.org/10.14403/jcms.2016.29.3.509

STUDY ON THE ARITHMETIC OF MODULAR FORMS

Choi, SoYoung (Department of Mathematics Education and RINS Gyeongsang National University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.29, no.3, 2016 , pp. 509-514 More about this Journal

Abstract

By constructing a canonical basis for the space $M_k^{\sharp}({\Gamma}_0(N))$ explicitly, we find a basis of the space of cusp forms for ${\Gamma}_0(N)$ consisting of $Poincar{\acute{e}}$ series.

Keywords

weakly holomorphic modular form; $Poincar{\acute{e}}$ series;

Citations & Related Records

Reference

1	J. Ahn and S. Choi, Arithmetic of weakly holomorphic modular forms for Hecke groups, JP Journal of Algebra, Number Theory and Application 37 (2015), no. 2, 105-124. DOI
2	J. H. Bruinier, K. Ono, R. C. Rhoades, and C. Robert, Differential operators for harmonic weak Maass forms and the vanishing of Hecke eigenvalues, Math. Ann. 342 (2008), no. 3, 673-693. DOI
3	D. Choi, Spaces of modular forms generated by eta-quotients, Ramanujan J. 14 (2007), no. 1, 69-77. DOI
4	H. Iwaniec, Topics in classical automorphic forms, Graduate Studies in Mathematics, 17. American Mathematical Society, Providence, RI, 1997.
5	T. Miyake, Modular forms, Springer, 1989
6	C. R. Rhoades, Linear relations among Poincare series via harmonic weak Maass forms, Ramanujan J. 29 (2012), no. 1-3, 311-320. DOI